1
The same base means —
💡 Hint:
The side is common.
Explanation:
One whole common side.
Class 9 · Maths · Chapter 9 · बिहार बोर्ड (BSEB)CBSE · NCERT 2026-27
Areas of Parallelograms and Triangles
Areas of Parallelograms and Triangles
How to use this page:
1. Read — Same base · Exercise 9.1 · Activity 1 · Activity 2 · Theorem 9.1 · Exercise 9.2 · triangles · Exercise 9.3 · Exercise 9.4, diagram, worked example, board tip
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3. Mastery ★ — all of that lesson correct. Redo the wrong ones
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- 1 The same base and the same parallels
- 2 Exercise 9.1 — reading the figures
- 3 Activity 1, Activity 2 and Theorem 9.1
- 4 The area formula
- 5 Exercise 9.2
- 6 Triangles and a median
- 7 Exercise 9.3 and optional 9.4
- Chapter winner — every lesson at mastery ★
🎬 Shorts
This chapter has no Short on the channel yet, so ten empty cards are not shown. The notes, diagrams and checks are complete.
📄 PDF download — notes + answer key
The same base and the same parallels
एक ही आधार और एक ही समांतर रेखाएँ · Textbook 9.2 · base · parallels
A common side and the parallel line above itNotes
Two figures are on the same base when one whole side belongs to both. One shared vertex is not one base. They lie between the same parallels when the other vertices lie on one line parallel to that base.
Equal bases also work. If two different segments are equal in length and lie on one line, later theorems take them too. On a figure, check that the upper points really sit on that parallel. A common side is not enough if a vertex lies on a different line.
Worked exampleExample
Question: Parallelogram ABCD and triangle PDC have base DC in common. P and A lie on a line parallel to DC. Are both between the same parallels?
Test: common base DC, and the other vertices on one line parallel to DC.
Conclusion: yes. The base is DC and the upper vertices lie on that parallel.
10-second revision
- Same base = one whole common side
- The other vertices lie on a parallel
- Equal bases work in the later theorems
Board tip · BSEBBoard tip
Do not write one shared point as the base. A base is a side.
Board tip · CBSEBoard tip
If the upper line is not parallel to the base, as in the book’s warning figures, do not write “the same parallels”.
Check your understandingall correct = mastery ★
2
If the other vertices lie on a line parallel to the base, the figures lie between the same parallels.
Explanation:
True.
3
The same base is a ______, not a point.
💡 Hint:
A whole side.
Explanation:
A side.
4
If two equal segments lie on one line, a later theorem treats them as —
💡 Hint:
Equal length.
Explanation:
Equal bases.
5
Write the two conditions for the same base and the same parallels.
Model answer (board format)
One side belongs to both figures. The other vertices lie on a line parallel to that side.
Check your answer:
6
Any two figures that share one point are on the same base.
Explanation:
False — a base is one whole side.
Exercise 9.1 — reading the figures
अभ्यास 9.1 — चित्र पहचानना · Textbook 9.2 · Exercise 9.1
Check two facts separately on every figureNotes
Exercise 9.1 asks which figures are on the same base and between the same parallels. Look at the base first, then at the upper line. If one condition holds and the other does not, the answer is no.
The pair may be a trapezium and a parallelogram, two parallelograms, two triangles, or a triangle and a parallelogram. The names may differ. The rule depends on the base and the parallels, not on the name.
Exercise 9.1 — yes or no, with a reasonActivity
Write two lines on each figure. First: the name of the common side, or the fact that the bases differ. Second: the line on which the other vertices lie, and whether it is parallel to the base. The pair meets the test only when both answers are yes.
Worked exampleExample
Question: Two triangles share base BC. The third vertices lie on a line that is not parallel to BC. Does the pair meet the test?
Check: the base is the same. The parallel condition fails.
Conclusion: no. The same base is not enough when the upper line is not parallel.
10-second revision
- Two conditions, both required
- Not the name: the base and the parallels
- Exercise 9.1 comes before the theorems
Board tip · BSEBBoard tip
Do not pass a figure by writing only “same base”. The second line must be about the parallel.
Board tip · CBSEBoard tip
Where the book says the figures are not between the same parallels, do not go on by assuming equal areas.
Check your understandingall correct = mastery ★
1
In Exercise 9.1 a pair counts only when —
💡 Hint:
Two conditions.
Explanation:
Both the base and the parallels.
2
If the base is the same but the upper line is not parallel, the test is still met.
Explanation:
False — both conditions are required.
3
Exercise 9.1 comes ______ Theorem 9.1.
💡 Hint:
The book order.
Explanation:
Before.
4
In a figure the base is common and the vertices are not on a parallel. Write the answer in two lines.
Model answer (board format)
The base is the same. The parallel condition fails, so the pair is not between the same parallels.
Check your answer:
Activity 1, Activity 2 and Theorem 9.1
क्रियाकलाप 1, क्रियाकलाप 2 और प्रमेय 9.1 · Textbook 9.3 · Activity 1 · Activity 2 · Theorem 9.1
Equal height gives equal areaNotes
Theorem 9.1: parallelograms on the same base, or on equal bases, and between the same parallels have equal areas. The height is the same for both, because the perpendicular distance between parallel lines is fixed.
The converse is also true. Equal bases and equal areas put the parallelograms between the same parallels. The proof uses the area formula: if the base is the same and the area is the same, the height is the same.
Activity 1 and Activity 2Activity
Activity 1 asks you to draw parallelograms ABCD and PQCD on a graph sheet. Match the areas by counting squares. Activity 2 cuts a parallelogram from thick paper and moves one piece. Both checks come before Theorem 9.1. Do not swap the numbers 1 and 2. A count is a check of the figure, not the proof.
Worked exampleExample
Question: ABCD and EFCD are on the same base DC and between the same parallels. ar(ABCD) = 24 cm². Find ar(EFCD).
Theorem: 9.1, the areas are equal.
Substitution: ar(EFCD) = 24 cm². The unit is the square centimetre.
10-second revision
- Theorem 9.1: the areas are equal
- Activity 1 is the graph sheet, Activity 2 is the cut paper
- Converse: equal areas, the same parallels
Board tip · BSEBBoard tip
Do not halve 24 cm². Theorem 9.1 says the parallelograms are equal, not half.
Board tip · CBSEBoard tip
Do not write the square count in place of the theorem. Write that the count agrees with 9.1.
Check your understandingall correct = mastery ★
1
Theorem 9.1 is about which figures?
💡 Hint:
The same base.
Explanation:
Parallelograms.
2
Activity 1 is on a graph sheet and Activity 2 is on cut paper.
Explanation:
True — that is the order.
3
If ar(ABCD) = 24 cm² and the conditions match, ar(EFCD) = ______ cm².
💡 Hint:
Equal.
Explanation:
24.
4
Equal bases and equal areas imply —
💡 Hint:
The converse.
Explanation:
Between the same parallels.
5
Write Theorem 9.1. Separate Activity 1 and Activity 2 in one line each.
Model answer (board format)
Parallelograms on the same base and between the same parallels have equal areas. Activity 1 counts squares. Activity 2 cuts paper and matches the pieces.
Check your answer:
The area formula
क्षेत्रफल का सूत्र · Textbook 9.3 · base × height
The height is perpendicular to that baseNotes
Area of a parallelogram = base × corresponding height. The height is perpendicular to the base side. Do not take a slanted side as the height. In a rectangle the perpendicular side is the height.
On the same base and between the same parallels, the triangle has half the area of the parallelogram. So the triangle is (1/2) × base × height. Give the answer in square centimetres when the sides are in centimetres.
Worked exampleExample
Question: Base DC = 8 cm and the corresponding height AL = 5 cm. Find the area of the parallelogram and of a triangle on the same base.
Formula: parallelogram = base × height. The triangle is half.
Substitution: 8 cm × 5 cm = 40 cm². The triangle = (1/2) × 40 cm² = 20 cm².
10-second revision
- Area = base × height
- The height is perpendicular, not a slanted side
- The triangle is half, 20 cm² when the parallelogram is 40 cm²
Board tip · BSEBBoard tip
Write 8 × 5 = 40 and put the unit cm². Only 40 without the unit is incomplete.
Board tip · CBSEBoard tip
Do not turn a slanted side of 6 cm into the height when the perpendicular 5 cm is given. The formula uses the corresponding height.
Check your understandingall correct = mastery ★
1
The area of a parallelogram is —
💡 Hint:
A product.
Explanation:
Base × height.
2
The height is perpendicular to the base.
Explanation:
True — a slanted side is not the height by itself.
3
8 cm × 5 cm = ______ cm².
💡 Hint:
Multiply.
Explanation:
40.
4
If the parallelogram is 40 cm², the triangle on the same base and parallels is —
💡 Hint:
Half.
Explanation:
20 cm².
5
Find the area of a parallelogram with base 12 cm and height 4 cm. Write the formula.
Model answer (board format)
Area = base × height = 12 cm × 4 cm = 48 cm².
Check your answer:
6
The area of a triangle is always equal to the area of a parallelogram.
Explanation:
False — on the same base and between the same parallels it is half.
Exercise 9.2
अभ्यास 9.2 · Textbook 9.3 · Exercise 9.2
Draw the perpendicular, then use Theorem 9.1Notes
Exercise 9.2 gives a perpendicular on a parallelogram, an interior point, and two parallelograms together. Before writing equal areas, name both the base and the parallels. A rectangle is also a parallelogram, so Theorem 9.1 runs on it too.
An interior point can make two triangles whose areas differ. Write them equal only when the base and the height really match.
Exercise 9.2 — showing the areas equalActivity
In each question first write the common base or the equal bases. Then write the line that is parallel. After that, Theorem 9.1. If numbers are given, do base × height and keep the unit cm². Exercise 9.3 is not yet. It comes after the triangles.
Worked exampleExample
Question: Rectangle EFCD and parallelogram ABCD stand on base DC. DC = 6 cm and the height is 4 cm. Write both areas.
Formula: area = 6 cm × 4 cm. Theorem 9.1 makes them equal.
Substitution: each = 24 cm².
10-second revision
- Exercise 9.2 is about parallelograms
- Theorem 9.1 also runs on a rectangle
- 9.3 comes later
Board tip · BSEBBoard tip
Do not leave the base unnamed and skip the theorem number. Write 9.1.
Board tip · CBSEBoard tip
24 cm² belongs to both. Writing 24 for one and 12 for the other is the mistake of halving.
Check your understandingall correct = mastery ★
1
Exercise 9.2 is mainly about —
💡 Hint:
After section 9.3.
Explanation:
The area of a parallelogram.
2
Theorem 9.1 does not run on a rectangle because a rectangle is not a parallelogram.
Explanation:
False — a rectangle is a parallelogram.
3
6 cm × 4 cm = ______ cm².
💡 Hint:
Multiply.
Explanation:
24.
4
Two parallelograms are on the same base and one has area 18 cm². Write the other. Name the reason.
Model answer (board format)
The other is also 18 cm², if they lie between the same parallels. The reason is Theorem 9.1.
Check your answer:
Triangles and a median
त्रिभुज और माध्यिका · Textbook 9.4 · Theorem 9.2 · Theorem 9.3
Triangles on that same height are equal tooNotes
Theorem 9.2: triangles on the same base, or on equal bases, and between the same parallels have equal areas. Theorem 9.3 is the converse: equal areas and the same base put the triangles between the same parallels.
A median halves the base. The height of both small triangles stays the same. So each area = (1/2) × the area of the whole triangle. Half the base times the same height gives that.
Worked exampleExample
Question: AD is a median and ar(ABC) = 30 cm². Find ar(ABD).
Formula: a median halves the area. ar(ABD) = (1/2) × ar(ABC).
Substitution: (1/2) × 30 cm² = 15 cm². ar(ACD) is 15 cm² as well.
10-second revision
- Theorem 9.2: the triangles have equal areas
- Theorem 9.3 is the converse
- A median halves the area
Board tip · BSEBBoard tip
Half of 30 cm² is 15 cm². Write both small triangles, and do not leave one at 30.
Board tip · CBSEBoard tip
The converse 9.3 is for when the areas are given equal and you must prove the parallels. 9.2 is the other direction.
Check your understandingall correct = mastery ★
1
Two triangles on the same base and parallels are —
💡 Hint:
Theorem 9.2.
Explanation:
Equal area.
2
A median divides the area of a triangle into two equal parts.
Explanation:
True — the base is halved and the height is the same.
3
If the whole triangle is 30 cm², one part by the median is ______ cm².
💡 Hint:
Half.
Explanation:
15.
4
Theorem 9.3 says —
💡 Hint:
The converse.
Explanation:
The parallels are proved.
5
ar(ABC) = 48 cm² and AD is a median. Write both small areas.
Model answer (board format)
Each = 48 cm² / 2 = 24 cm². ar(ABD) = ar(ACD) = 24 cm².
Check your answer:
Exercise 9.3 and optional 9.4
अभ्यास 9.3 और वैकल्पिक 9.4 · Textbook · Exercise 9.3 · Exercise 9.4
The triangles first, the optional set afterNotes
Exercise 9.3 asks for a median, triangles on the same base, and adding areas along a row of parallels. Each time write the number of Theorem 9.2 or 9.3. If there is a median, use half the area.
Exercise 9.4 is optional, and the number does not change. One question places a parallelogram and a rectangle on the same base. In the later links one result leads toward Pythagoras. The book says a simpler proof comes later. Equality of areas is enough here.
Exercise 9.3, then Exercise 9.4Activity
Finish 9.3 first. Pick out the triangles on both sides of a point on the median. Then 9.4. If a rectangle and a parallelogram share the base, use Theorem 9.1. Do not give the Pythagoras line a new theorem number now. The book leaves it for later.
Worked exampleExample
Question: AD is a median and ar(ABC) = 40 cm². Find each of ar(ABD) and ar(ACD).
Formula: the median gives ar(ABD) = ar(ACD) = half.
Substitution: 40 cm² / 2 = 20 cm² each. The unit is cm².
10-second revision
- Exercise 9.3 is about triangles
- Exercise 9.4 is optional and stays numbered 9.4
- The Pythagoras line waits for a later proof
Board tip · BSEBBoard tip
Do not merge 9.4 into 9.3 as one number. The book keeps both.
Board tip · CBSEBoard tip
Half of 40 is 20. Both small triangles are 20 cm² each. Writing 40 for one leaves out the median.
Check your understandingall correct = mastery ★
1
After Exercise 9.3 comes —
💡 Hint:
The book order.
Explanation:
Exercise 9.4.
2
Exercise 9.4 is optional, so it should be written as 9.3.
Explanation:
False — the number stays 9.4.
3
Half of 40 cm² is ______ cm².
💡 Hint:
Divide by 2.
Explanation:
20.
4
A rectangle and a parallelogram on the same base have areas that are —
💡 Hint:
Theorem 9.1.
Explanation:
Equal, when the parallels are the same.
5
Write the order of Exercises 9.1 to 9.4 and say which one is optional.
Model answer (board format)
The order is 9.1, 9.2, 9.3, then 9.4. The optional one is 9.4.
Check your answer:
6
This chapter does not claim that the simpler proof of the Pythagoras line is finished here.
Explanation:
True — the book leaves the simpler proof for later.
❓ Full question bank — with answers and explanations — 66 questions
Pick a type. The 36 lesson checks are separate — each lesson has as many as its topic needs. All correct earns mastery ★.
BSEB modelpractice · not annual60 tried · 0 correctMultiple choiceMCQ130 tried · 0 correctTrue / falseTrue / false80 tried · 0 correctFill in the blanksFill80 tried · 0 correctMatchMatch20 tried · 0 correctAssertion–reasonAssertion–reason50 tried · 0 correctBalancingBalancing40 tried · 0 correctIdentifyIdentify20 tried · 0 correctShort and longVSA, SA, LA120 tried · 0 correctCBSE-stylenot a PYQ60 tried · 0 correct
No question is marked as a verified past paper. The BSEB set is a model for practice. CBSE items are CBSE-style, not a copy of any year’s paper.
Multiple choice
0/13Pick one option. A wrong try brings a hint.
1
The same base is —
💡 Hint:
A whole side.
Explanation:
A common side.
2
Theorem 9.1 equates —
💡 Hint:
The same base.
Explanation:
The areas.
3
The area formula is —
💡 Hint:
The product.
Explanation:
Base × height.
4
The area of 8 × 5 is —
💡 Hint:
Multiply.
Explanation:
40 cm².
5
The triangle on the 40 cm² parallelogram is —
💡 Hint:
Half.
Explanation:
20 cm².
6
Theorem 9.2 is about —
💡 Hint:
The same base.
Explanation:
Areas of triangles.
7
A median divides the area —
💡 Hint:
Half the base.
Explanation:
Two equal parts.
8
Half of 30 cm² is —
💡 Hint:
Divide by 2.
Explanation:
15 cm².
9
Activity 1 is —
💡 Hint:
The order.
Explanation:
A graph sheet.
10
Exercise 9.4 is —
💡 Hint:
The book.
Explanation:
Optional 9.4.
11
The height is —
💡 Hint:
The corresponding height.
Explanation:
Perpendicular.
12
From equal areas and the same base —
💡 Hint:
Theorem 9.3.
Explanation:
The parallels.
13
The area of 6 × 4 is —
💡 Hint:
Multiply.
Explanation:
24 cm².
True or false
0/81
One common point is called the same base.
Explanation:
False — a base is a side.
2
Theorem 9.1 says the areas of the parallelograms are equal.
Explanation:
True.
3
A slanted side is always the height.
Explanation:
False — the height is perpendicular to the base.
4
On the same base and parallels, the triangle is half the parallelogram.
Explanation:
True.
5
Activity 2 comes before Activity 1.
Explanation:
False — the graph sheet comes first, then the cut paper.
6
A median does not split the area.
Explanation:
False — two equal areas are formed.
7
Exercise 9.4 keeps the number 9.4.
Explanation:
True — it is optional.
8
A rectangle is not a parallelogram.
Explanation:
False — a rectangle is a parallelogram, so Theorem 9.1 applies.
Fill in the blanks
0/81
Area = base × ______ .
💡 Hint:
The perpendicular distance.
Explanation:
Height.
2
8 × 5 = ______ .
💡 Hint:
Multiply.
Explanation:
40.
3
Half of 40 cm² is ______ cm².
💡 Hint:
The triangle.
Explanation:
20.
4
Theorem ______ states equal areas of parallelograms.
💡 Hint:
Triangles are 9.2.
Explanation:
9.1.
5
One part of 30 cm² by the median is ______ cm².
💡 Hint:
Half.
Explanation:
15.
6
6 × 4 = ______ .
💡 Hint:
Multiply.
Explanation:
24.
7
The theorem number for triangles is ______.
💡 Hint:
The converse is 9.3.
Explanation:
9.2.
8
The optional exercise number is ______.
💡 Hint:
After 9.3.
Explanation:
9.4.
Match
0/21
Match the number with the job.
Column B: A. Optional exercise · B. Areas of parallelograms · C. Areas of triangles · D. Graph sheet
1. 9.1
2. 9.2
3. Activity 1
4. 9.4
Explanation:
9.1 is parallelograms, 9.2 triangles, Activity 1 the graph, and 9.4 optional.
2
Match the formula with the figure.
Column B: A. Perpendicular to the base · B. Base × height · C. (1/2) × parallelogram · D. Two equal areas
1. Parallelogram
2. Triangle half
3. Median
4. Height
Explanation:
The parallelogram is a product, the triangle is half, the median makes two equal parts, and the height is perpendicular.
Assertion–reason
0/5Check both statements, then see whether the reason explains the assertion.
1
Assertion (A): Parallelograms on the same base and parallels have equal areas.
Reason (R): Both have the same height, so base × height is the same.
Explanation:
Both are true and R is the reason.
2
Assertion (A): A median halves the area.
Reason (R): The angles of a quadrilateral add to 360°.
Explanation:
A is true. R may be true, but it does not explain this reason.
3
Assertion (A): The triangle is half the parallelogram on the same base.
Reason (R): The area of the triangle is always greater than the parallelogram.
Explanation:
A is true. R is false.
4
Assertion (A): One common point is a sufficient base.
Reason (R): The same base is one whole common side.
Explanation:
A is false. R is true.
5
Assertion (A): Triangles of equal area on the same base can lie between the same parallels.
Reason (R): Theorem 9.3 proves the parallels from equal areas.
Explanation:
Both are true and R is the explanation.
Coefficient practice
0/4These are not results of this maths chapter. They are only coefficient practice for H2 + O2 → H2O.
1
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). This is not an area result.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
2
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). Match the hydrogen count.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
3
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). Match the oxygen count.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
4
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). A blank coefficient is 1.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
Classify
0/21
Place each pair in the right decision. Assume the same parallels where stated.
Common side and parallels
Only a common point
Same base, line not parallel
Equal bases and the same parallels
Explanation:
A common side or equal bases, with the parallels, meet the test. A point alone is not enough.
2
Place each statement on the theorem.
Parallelograms, equal area
Triangles, equal area
Optional exercise
Parallelograms with the same height
Explanation:
Parallelograms are 9.1. Triangles are 9.2. The optional set is 9.4.
Very short answer
0/51
Write the formula for the area of a parallelogram.
Model answer (board format)
Base × corresponding height.
Check your answer:
2
Write Theorem 9.1 in one line.
Model answer (board format)
Parallelograms on the same base and between the same parallels have equal areas.
Check your answer:
3
Find the area for base 9 cm and height 2 cm.
Model answer (board format)
9 cm × 2 cm = 18 cm².
Check your answer:
4
Name Activity 1 and Activity 2 in order.
Model answer (board format)
First the graph sheet, then the cut paper.
Check your answer:
5
What does a median do to the area?
Model answer (board format)
It divides it into two equal parts.
Check your answer:
Short answer
0/41
Base 8 cm, height 5 cm. Write the areas of both the parallelogram and the triangle.
Model answer (board format)
The parallelogram = 8 × 5 = 40 cm². The triangle = 20 cm².
Check your answer:
2
ar(ABC) = 36 cm² and AD is a median. Write ar(ABD) and ar(ACD).
Model answer (board format)
Each is 18 cm².
Check your answer:
3
Two parallelograms are on the same base. One has area 27 cm². Write the other and the theorem.
Model answer (board format)
If the parallels are the same, the other is also 27 cm². Theorem 9.1.
Check your answer:
4
In Exercise 9.1 one figure has a common base but the line is not parallel. Write the decision.
Model answer (board format)
The test is incomplete. They are not between the same parallels, so do not write the areas as equal.
Check your answer:
Long answer
0/31
Write Theorem 9.1 and the area formula. For base 10 cm and height 3 cm find the parallelogram and the half triangle.
Model answer (board format)
On the same base and parallels the areas are equal. The formula is base × height. 10 × 3 = 30 cm². The triangle = 15 cm².
Check your answer:
2
Write Theorems 9.2 and 9.3. Split a 50 cm² triangle by a median. Give the order of Activity 1 and Activity 2.
Model answer (board format)
9.2 equal areas of triangles. 9.3 the converse. Each part is 25 cm². Activity 1, the graph sheet, comes first, then Activity 2, the cut paper.
Check your answer:
3
Write the order of Exercises 9.1 to 9.4. Say why 9.4 is optional and why the Pythagoras line is not a finished proof here.
Model answer (board format)
The order is 9.1, 9.2, 9.3, 9.4. The book calls 9.4 optional, and the number stays. The simpler proof of the Pythagoras line is left for a later chapter.
Check your answer:
BSEB model paper · practice
0/6This model set is for practice. It is not a question from any year’s annual examination. Annual questions will be added only when a source page is available.
1
With base 7 cm and height 4 cm the area is —
💡 Hint:
7 × 4.
Explanation:
28 cm².
2
One part of 20 cm² in a triangle with a median means the whole is —
💡 Hint:
Double.
Explanation:
40 cm².
3
12 × 3 = ______ .
💡 Hint:
Multiply.
Explanation:
36.
4
Theorem 9.2 is about triangles.
Explanation:
True.
5
Base 16 cm, height 5 cm. Write the parallelogram area and the triangle on it.
Model answer (board format)
16 × 5 = 80 cm². The triangle = 40 cm².
Check your answer:
6
This is coefficient practice, not a result of the areas chapter. Balance H2 + O2 making H2O by filling coefficients (blank = 1).
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
CBSE-style questions
0/6These are competency-based practice questions. They are not copies of a CBSE paper.
1
A field is a parallelogram. The base is 20 m and the height is 8 m. The area is —
💡 Hint:
20 × 8.
Explanation:
160 m². The unit is square metres, not metres alone.
2
Two fields share one boundary and the far boundary is parallel. The right fact about the area is —
💡 Hint:
Theorem 9.1.
Explanation:
On the same base and parallels the areas are equal.
3
Assertion (A): On the same base the triangle has half the area of the parallelogram.
Reason (R): The three sides of a triangle add to 180.
Explanation:
A is true when the parallels are the same too. R is false. 180° is the sum of the angles.
4
Counting squares on a graph sheet is the full proof of Theorem 9.1.
Explanation:
False — the count is the check in Activity 1. The proof is in the theorem.
5
A rectangular tile and a slanted parallelogram tile share the base 12 cm. The height is 5 cm. Write both areas. Why not take the slanted side as the height?
Model answer (board format)
Both are 12 × 5 = 60 cm², Theorem 9.1. The slanted side is not perpendicular. The height is the 5 cm perpendicular to the base.
Check your answer:
6
The median of a triangular plot splits it into two parts. The whole area is 90 m². Write each part.
Model answer (board format)
Each part is 90 / 2 = 45 m². A median halves the area.
Check your answer:
🏛️ Board exam corner — Bihar Board (BSEB)— CBSE
Switch board with BSEB | CBSE above. The lessons follow the same NCERT chapter.
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CBSE-style · competency-based
These are case and assertion-reason practice items. Do not treat them as past CBSE questions.
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🧠 What you learned + equation sheet
What you learned
- The same base means a common side, and the other vertices lie on a line parallel to that base.
- Parallelograms on the same base and between the same parallels have equal areas.
- Area = base × corresponding height. The unit may be square centimetres.
- In that same setting the triangle has half the area of the parallelogram.
- Triangles on the same base and between the same parallels have equal areas.
- A median splits the area in half. Exercises 9.1 to 9.4 stay in that order.
| What | Keep this |
|---|---|
| Base | common side, or equal bases |
| Height | perpendicular to the base |
| Parallelogram | area = base × height |
| Theorem 9.1 | equal areas |
| Triangle | half the parallelogram |
| Median | two equal areas |
The notes are original writing. The textbook was used only for activity order and numbers. “Verified” will be used only on a question that has a source page.