1
If the height is known, the area of a triangle is —
💡 Hint:
Half a rectangle.
Explanation:
(1/2) × base × height.
Class 9 · Maths · Chapter 12 · बिहार बोर्ड (BSEB)CBSE · NCERT 2026-27
Heron's Formula
Heron's Formula
How to use this page:
1. Read — Area with height · Heron formula · Exercise 12.1 · quadrilaterals · Exercise 12.2, diagram, worked example, board tip
2. Check — each lesson has its own questions; the number follows the lesson
3. Mastery ★ — all of that lesson correct. Redo the wrong ones
4. The memory figure shows a triangle with sides a, b and c and the semi-perimeter s, from which the area comes out of a square root.
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- 1 When the height is known
- 2 Heron's formula
- 3 Exercise 12.1 — board, wall, and a ratio
- 4 The third side and the rent
- 5 A quadrilateral as two triangles
- 6 Exercise 12.2 — field, umbrella, trapezium
- 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
When the height is known
जब ऊँचाई पता हो · Textbook 12.1 · base × height
The old formula only when the height is givenNotes
The area of a rectangle or a square is length times breadth. For a triangle, area = (1/2) × base × height. The height is perpendicular to the base.
If a scalene park gives only three sides, the height does not appear at once. Pythagoras helps only when some angle is a right angle. Otherwise the next formula is needed.
Worked exampleExample
Question: The base is 10 cm and the height is 6 cm. Find the area of the triangle.
Formula: area = (1/2) × base × height.
Substitution: (1/2) × 10 × 6 = 30.
Unit: square centimetre.
10-second revision
- Area = (1/2) × b × h
- The height is perpendicular
- This formula stops when only the sides are known
Board tip · BSEBBoard tip
If the unit is the centimetre, the answer is the square centimetre. Do not leave centimetre and metre together.
Board tip · CBSEBoard tip
Forgetting the 1/2 and writing the rectangle area is a common slip.
Check your understandingall correct = mastery ★
2
If only three sides are given, the height formula applies at once.
Explanation:
False — the height is needed separately, or use Heron.
3
If the base is 8 cm and the height is 5 cm, the area is ______ square centimetres.
💡 Hint:
(1/2) × 8 × 5.
Explanation:
20 square centimetres.
4
Pythagoras gives the height when —
💡 Hint:
A right triangle.
Explanation:
When some angle is 90°.
5
The base is 12 m and the height is 7 m. Write the area with the formula, the substitution and the unit.
Model answer (board format)
Area = (1/2) × 12 × 7 = 42 square metres.
Check your answer:
Heron's formula
हीरोन का सूत्र · Textbook 12.2 · s · square root
The area from three sidesNotes
Heron's formula, also called Hero's formula, gives the area from three sides. s = (a + b + c) / 2 and the area = √[s(s − a)(s − b)(s − c)].
Find s first. Then the three differences. Then the square root of the product. The unit is the square of the side unit. If s − a is zero or negative, the sides are not a triangle.
Worked exampleExample
Question: The sides are 7 cm, 15 cm and 20 cm. Find the area.
Formula: s = (a + b + c) / 2, area = √[s(s − a)(s − b)(s − c)].
Substitution: s = (7 + 15 + 20) / 2 = 21 cm. The differences are 14, 6 and 1. √(21 × 14 × 6 × 1) = √1764 = 42.
Unit: square centimetre.
10-second revision
- s is half the perimeter
- The square root of four factors
- On 7, 15, 20 the area is 42
Board tip · BSEBBoard tip
Do not write s as the full perimeter. Division by 2 is required.
Board tip · CBSEBoard tip
Show the four numbers before the square root. Only the final 42 can lose half the marks.
Check your understandingall correct = mastery ★
1
s equals —
💡 Hint:
The semi-perimeter.
Explanation:
(a + b + c) / 2.
2
The Heron area is the square root of s(s − a)(s − b)(s − c).
Explanation:
True.
3
If the sides are 7, 15 and 20 cm, s is ______ cm.
💡 Hint:
42 ÷ 2.
Explanation:
21 cm.
4
The sides are 5 cm, 5 cm and 6 cm. Find s and the area.
Model answer (board format)
s = (5+5+6)/2 = 8 cm. √[8×3×3×2] = √144 = 12 square centimetres.
Check your answer:
Exercise 12.1 — board, wall, and a ratio
अभ्यास 12.1 — बोर्ड, दीवार और अनुपात · Exercise 12.1 · six questions
Six questions, one formulaNotes
Exercise 12.1 does not give the height. Each time find s, then the square root. If an equilateral board has side a, the area is (√3 / 4) a². If the perimeter is 180 cm, a = 60 cm.
The wall 122 m, 22 m, 120 m is nearly right-angled, because 22² + 120² = 122². Heron and (1/2)×22×120 give one area. Rent is area × rate × time. Three months are 3/12 = 1/4 of a year.
Exercise 12.1 in orderActivity
1) An equilateral board, side a, then perimeter 180 cm. 2) A wall 122 m, 22 m, 120 m and three months of rent. 3) A slide wall 15 m, 11 m, 6 m. 4) Two sides 18 cm and 10 cm, perimeter 42 cm. 5) Ratio 12 : 17 : 25, perimeter 540 cm. 6) Isosceles, perimeter 30 cm, equal sides 12 cm.
Worked exampleExample
Question: An equilateral side is 6 cm. Find the area by Heron.
Formula: s = 3a / 2, area = √[s(s − a)³] = (√3 / 4) a².
Substitution: s = 9 cm. √[9 × 3 × 3 × 3] = √243 = 9√3. (√3 / 4) × 36 = 9√3.
Unit: square centimetre.
10-second revision
- a = perimeter / 3 in an equilateral triangle
- 122, 22, 120 is a right-angle check
- Three months = 1/4 year
Board tip · BSEBBoard tip
Do not multiply 5000 by a full year if the months are three. Use 1/4.
Board tip · CBSEBoard tip
In the ratio 12 : 17 : 25 do not multiply each part by 540. First 12+17+25 = 54.
Check your understandingall correct = mastery ★
1
If an equilateral perimeter is 180 cm, the side is —
💡 Hint:
Three equal sides.
Explanation:
60 cm.
2
22² + 120² = 122², so the wall passes a right-angle check.
Explanation:
True — 484 + 14400 = 14884 = 122².
3
Three months are ______ of a year.
💡 Hint:
3/12.
Explanation:
1/4.
4
In the ratio 12 : 17 : 25 with perimeter 540 cm, one part is —
💡 Hint:
540 / 54.
Explanation:
10 cm. The sides are 120, 170 and 250 cm.
5
The perimeter is 42 cm and two sides are 18 cm and 10 cm. Write the third side and s.
Model answer (board format)
The third = 42 − 28 = 14 cm. s = 42 / 2 = 21 cm.
Check your answer:
6
If an isosceles perimeter is 30 cm and each equal side is 12 cm, the base stays 12 cm.
Explanation:
False — the base = 30 − 24 = 6 cm.
The third side and the rent
तीसरी भुजा और किराया · Numerical forms in Exercise 12.1
Subtract two sides from the perimeterNotes
If two sides and the perimeter are given, the third = perimeter − the sum of those two. Then s = perimeter / 2. Do not add s again from scratch with a new mistake.
A gate width is subtracted from the perimeter. The area does not shrink. A rate in rupees per metre multiplies the remaining length. A rate per square metre multiplies the area.
Worked exampleExample
Question: The sides are 13 cm, 14 cm and 15 cm. Find the area.
Formula: s = (a+b+c)/2, area = √[s(s−a)(s−b)(s−c)].
Substitution: s = 21 cm. √[21×8×7×6] = √7056 = 84.
Unit: square centimetre.
10-second revision
- The third side is what the perimeter leaves
- s = perimeter / 2
- The area of 13, 14, 15 is 84
Board tip · BSEBBoard tip
Do not cut a gate out of the area. It is cut from the length of the wire.
Board tip · CBSEBoard tip
Write square centimetres with 84. An answer without the unit stays incomplete.
Check your understandingall correct = mastery ★
1
If the perimeter is 32 cm and the sides are 8 and 11 cm, the third is —
💡 Hint:
32 − 19.
Explanation:
13 cm.
2
s is always half the perimeter.
Explanation:
True — that is the definition.
3
On 13, 14, 15 cm the area is ______ square centimetres.
💡 Hint:
√7056.
Explanation:
84 square centimetres.
4
If the gate is 3 m and the perimeter is 250 m, the wire is —
💡 Hint:
Subtract from the perimeter.
Explanation:
247 m.
5
The sides are 9 m, 10 m and 17 m. Write s and the check that a triangle does or does not form.
Model answer (board format)
s = 18 m. s − 17 = 1 > 0, and 9+10 > 17. A triangle forms. The area is still √[18×9×8×1].
Check your answer:
A quadrilateral as two triangles
चतुर्भुज को दो त्रिभुज · Textbook 12.3 · diagonal
One diagonal is enoughNotes
A field is often a quadrilateral. Four sides are not enough. Draw one diagonal and use Heron on both triangles. The sum of the two areas is the field.
A right-angled piece can also come from (1/2)×base×height. If Heron reaches the same number, the calculation is right. In hectares, 1 hectare = 10000 square metres.
Worked exampleExample
Question: A diagonal of 10 cm splits a quadrilateral into two triangles of sides 6, 8, 10 and 6, 8, 10. Find the area.
Formula: area of one right triangle = (1/2) × 6 × 8. Heron check: s = 12, √[12×6×4×2] = √576 = 24.
Substitution: one triangle is 24, both are 48.
Unit: square centimetre.
10-second revision
- A diagonal makes two triangles
- The sum is the whole area
- 1 hectare = 10000 m²
Board tip · BSEBBoard tip
The two triangles can have different values of s. Do not put one s on the whole quadrilateral.
Board tip · CBSEBoard tip
When changing into hectares, divide by 10000. Do not multiply.
Check your understandingall correct = mastery ★
1
In this chapter the area of a quadrilateral comes —
💡 Hint:
A diagonal splits it.
Explanation:
The sum of two triangles.
2
1 hectare is 10000 square metres.
Explanation:
True.
3
The area of one 6-8-10 triangle is ______ square centimetres.
💡 Hint:
(1/2)×6×8.
Explanation:
24 square centimetres.
4
Two triangles have areas 30 m² and 45 m². How many hectares is the field?
Model answer (board format)
The sum = 75 m². Hectares = 75 / 10000 = 0.0075 hectare.
Check your answer:
Exercise 12.2 — field, umbrella, trapezium
अभ्यास 12.2 — खेत, छाता, समलंब · Exercise 12.2 · nine questions
Nine questions, all by splittingNotes
Exercise 12.2 asks for quadrilaterals, a parallelogram, a rhombus, an umbrella, a kite, tiles and a trapezium. Split each figure into triangles. If the base and the area match, the height of the parallelogram = area of the triangle ÷ base.
The non-parallel sides of a trapezium are used to find the height. The height is perpendicular. Then area = (1/2) × (sum of the parallel sides) × height. A polish rate in paise per square centimetre multiplies the area.
Exercise 12.2 in orderActivity
1) A quadrilateral, angle C = 90°, sides 9 m, 12 m, 5 m, 8 m. 2) Sides 3, 4, 4, 5 cm and diagonal 5 cm. 3) An aeroplane picture, the sum of the pieces. 4) A triangle 26, 28, 30 cm and a parallelogram on the same base 28 cm. 5) A rhombus of side 30 m, longer diagonal 48 m, 18 cows. 6) Ten umbrella pieces, each 20, 50, 50 cm. 7) A kite, a square diagonal 32 cm and an isosceles piece. 8) 16 tiles, sides 9, 28, 35 cm, rate 50 paise per cm². 9) A trapezium, parallel sides 25 m and 10 m, the others 14 m and 13 m.
Worked exampleExample
Question: A triangle has area 168 square centimetres and the same base is 28 cm. Find the height of the parallelogram.
Formula: height = area ÷ base.
Substitution: 168 ÷ 28 = 6.
Unit: centimetre.
10-second revision
- For equal areas, height = area / base
- Trapezium = (1/2)(a+b)h
- A rate multiplies the area
Board tip · BSEBBoard tip
Dividing the area by 18 cows is the last step. Only the whole field is half an answer.
Board tip · CBSEBoard tip
Do not add the non-parallel sides straight into (a+b). They are used to find the height.
Check your understandingall correct = mastery ★
1
If the area and the base 28 cm are shared, the height is —
💡 Hint:
Area = base × height.
Explanation:
Area ÷ 28.
2
The area of a trapezium is (1/2) × (sum of the parallel sides) × height.
Explanation:
True.
3
168 ÷ 28 = ______ cm.
💡 Hint:
The height.
Explanation:
6 cm.
4
A rate of 50 paise per cm² multiplies —
💡 Hint:
Per square centimetre.
Explanation:
The area. If there are 16 tiles, first one area, then 16.
5
The parallel sides of a trapezium are 10 m and 6 m and the height is 4 m. Write the area.
Model answer (board format)
(1/2) × (10+6) × 4 = (1/2) × 16 × 4 = 32 square metres.
Check your answer:
6
Four sides without a diagonal fix the area of a quadrilateral.
Explanation:
False — a diagonal or a right angle is needed, then two triangles.
❓ Full question bank — with answers and explanations — 66 questions
Pick a type. The 30 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
If the height is known, the area is —
💡 Hint:
Half the product.
Explanation:
(1/2) × b × h.
2
s is —
💡 Hint:
The semi-perimeter.
Explanation:
(a+b+c)/2.
3
The Heron area is —
💡 Hint:
Do not forget the square root.
Explanation:
√[s(s−a)(s−b)(s−c)].
4
On an equilateral side a the area is —
💡 Hint:
Heron simplifies.
Explanation:
(√3 / 4) a².
5
The side of an equilateral triangle of perimeter 180 cm is —
💡 Hint:
180 / 3.
Explanation:
60 cm.
6
Three months are —
💡 Hint:
3/12.
Explanation:
1/4 of a year.
7
In 12 : 17 : 25 with perimeter 540, one part is —
💡 Hint:
540 / 54.
Explanation:
10 cm.
8
The area of 13, 14, 15 cm is —
💡 Hint:
√7056.
Explanation:
84 square centimetres.
9
The area of 7, 15, 20 cm is —
💡 Hint:
√1764.
Explanation:
42 square centimetres.
10
1 hectare is —
💡 Hint:
Square metres.
Explanation:
10000 square metres.
11
For an equal area the height is —
💡 Hint:
168 ÷ 28 = 6.
Explanation:
Area ÷ base.
12
The area of a trapezium is —
💡 Hint:
The parallel sides are a and b.
Explanation:
(1/2)(a+b)h.
13
A gate is subtracted from —
💡 Hint:
The length of the wire.
Explanation:
The perimeter.
True or false
0/81
s is the full perimeter.
Explanation:
False — s is half the perimeter.
2
If s − a is negative, the area is still real.
Explanation:
False — the sides do not make a triangle.
3
22² + 120² = 122².
Explanation:
True — the right-angle check for the wall.
4
For an isosceles perimeter 30 cm and equal sides 12 cm, the base is 6 cm.
Explanation:
True — 30 − 24 = 6.
5
Four sides without a diagonal fix the area.
Explanation:
False — two triangles are needed.
6
A rate per square metre multiplies the area.
Explanation:
True.
7
The area of a 6-8-10 triangle is 48.
Explanation:
False — (1/2)×6×8 = 24.
8
Heron and (1/2)bh can give one answer on a right triangle.
Explanation:
True — that is the way to check.
Fill in the blanks
0/81
For base 10 cm and height 6 cm the area is ______.
💡 Hint:
(1/2)×10×6.
Explanation:
30.
2
Half of 7+15+20 is s = ______.
💡 Hint:
42/2.
Explanation:
21.
3
The area of 5, 5, 6 cm is ______ square centimetres.
💡 Hint:
√144.
Explanation:
12.
4
The side of an equilateral perimeter 180 cm is ______ cm.
💡 Hint:
180/3.
Explanation:
60.
5
Subtracting 18 and 10 from perimeter 42 leaves the third side ______ cm.
💡 Hint:
42−28.
Explanation:
14.
6
The area of 13, 14, 15 is ______.
💡 Hint:
√7056.
Explanation:
84.
7
168 ÷ 28 = ______.
💡 Hint:
The height.
Explanation:
6.
8
1 hectare = ______ square metres.
💡 Hint:
Four zeros.
Explanation:
10000.
Match
0/21
Match the demand with the right measure.
Column B: A. (√3 / 4) a² · B. Area · C. Perimeter, after the gate · D. (1/2)(a+b)h
1. Grass
2. Fence
3. Trapezium
4. Equilateral
Explanation:
Grass is area, a fence is perimeter, a trapezium uses the average height, and an equilateral triangle uses the √3 formula.
2
Match the exercise number with its job.
Column B: A. Trapezium · B. Equilateral board · C. Ratio 12 : 17 : 25 · D. Parallelogram on the same base
1. 12.1 question 1
2. 12.1 question 5
3. 12.2 question 4
4. 12.2 question 9
Explanation:
The board is first, the ratio is fifth, the same base is fourth, and the trapezium is ninth.
Assertion–reason
0/5Check both statements, then see whether the reason explains the assertion.
1
Assertion (A): Heron gives the area from three sides.
Reason (R): s = (a+b+c)/2 and the area is the square root of the four factors.
Explanation:
Both are true and R is the reason.
2
Assertion (A): On a right triangle (1/2)bh and Heron can give one answer.
Reason (R): Four sides of a quadrilateral are enough without a diagonal.
Explanation:
A is true. R is false.
3
Assertion (A): A gate is subtracted from the perimeter.
Reason (R): A gate also subtracts the same number from the area.
Explanation:
A is true. R is false — the area does not shrink.
4
Assertion (A): s is the full perimeter.
Reason (R): s is half the sum of the three sides.
Explanation:
A is false. R is true.
5
Assertion (A): For equal areas the parallelogram height is area ÷ base.
Reason (R): The area of a parallelogram is base × height.
Explanation:
Both are true and R explains A.
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 demand on the right quantity.
Planting grass
A wire fence
Polish
Leaving a gate
Explanation:
Grass and polish are area. A fence and a gate are perimeter.
2
Place each question on its exercise.
Equilateral board
Ratio 12 : 17 : 25
Trapezium field
Umbrella cloth
Explanation:
The board and the ratio are in 12.1. The trapezium and the umbrella are in 12.2.
Very short answer
0/51
Write the formula for s.
Model answer (board format)
s = (a + b + c) / 2.
Check your answer:
2
Write the Heron area.
Model answer (board format)
√[s(s − a)(s − b)(s − c)].
Check your answer:
3
Base 8 cm, height 5 cm. Write the area.
Model answer (board format)
(1/2) × 8 × 5 = 20 square centimetres.
Check your answer:
4
How many square metres is 1 hectare?
Model answer (board format)
10000 square metres.
Check your answer:
5
Write the area of an equilateral side a.
Model answer (board format)
(√3 / 4) a².
Check your answer:
Short answer
0/41
Sides 7 cm, 15 cm, 20 cm. Find s and the area.
Model answer (board format)
s = 21 cm. √(21×14×6×1) = √1764 = 42 square centimetres.
Check your answer:
2
Perimeter 42 cm, sides 18 and 10 cm. Write the third side and s.
Model answer (board format)
The third = 14 cm. s = 21 cm.
Check your answer:
3
Two triangles are 24 square centimetres each. Write the quadrilateral. If the measures were m², what would the hectare step be? Here the unit is cm², so write only the sum, and name the hectare divisor.
Model answer (board format)
The sum = 48 square centimetres. For hectares, square metres are divided by 10000.
Check your answer:
4
Area 168 cm² and base 28 cm. Find the parallelogram height.
Model answer (board format)
Height = 168 ÷ 28 = 6 cm.
Check your answer:
Long answer
0/31
Write Heron's formula. On an equilateral triangle of side 6 cm show s and the area.
Model answer (board format)
s = (a+b+c)/2, area = √[s(s−a)(s−b)(s−c)]. s = 9 cm. √243 = 9√3 square centimetres. This is the same as (√3/4)×36.
Check your answer:
2
Write the six jobs of Exercise 12.1 in order, one line each.
Model answer (board format)
1) Equilateral board, then perimeter 180 cm. 2) Wall 122, 22, 120 m and three months of rent. 3) Wall 15, 11, 6 m. 4) 18 cm, 10 cm, perimeter 42 cm. 5) Ratio 12:17:25, perimeter 540 cm. 6) Isosceles, perimeter 30 cm, equal side 12 cm.
Check your answer:
3
How will you split a quadrilateral? Write the area of two 6-8-10 triangles and the area of a trapezium 10 m, 6 m, height 4 m.
Model answer (board format)
One diagonal makes two triangles. One 6-8-10 triangle has area 24, both have 48 square centimetres. The trapezium (1/2)×(10+6)×4 = 32 square metres.
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
The area of 5, 5, 6 cm is —
💡 Hint:
√144.
Explanation:
12 square centimetres.
2
If the ratio parts add to 54 and the perimeter is 540, one part is —
💡 Hint:
540/54.
Explanation:
10.
3
If the equal sides are 12 and 12 and the base is 6 cm, the perimeter is ______ cm.
💡 Hint:
12+12+6.
Explanation:
30.
4
Rent is area × rate × time.
Explanation:
True. If the months are three, the time is 1/4 year.
5
Write the area of an equilateral triangle of side 6 cm by (√3 / 4) a².
Model answer (board format)
(√3 / 4) × 36 = 9√3 square centimetres.
Check your answer:
6
This is coefficient practice, not a result of Heron's formula. 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 student multiplies the area by 20 for a fence. The correction is —
💡 Hint:
A fence is a length.
Explanation:
A rate per metre applies to the perimeter.
2
A field is a quadrilateral and only four fence lengths are known. What else is needed for the area?
💡 Hint:
Two triangles.
Explanation:
A diagonal or a right angle.
3
Assertion (A): The cost of polish is on the area.
Reason (R): Polish is also charged on the perimeter at the same rate.
Explanation:
A is true. R is false — a rate per square centimetre asks for the area.
4
The ratio 12 : 17 : 25 means the sides are 12 cm, 17 cm and 25 cm, even if the perimeter is 540 cm.
Explanation:
False — one part is 10 cm. The sides are 120, 170 and 250 cm.
5
The sides of a park are 20 m, 21 m and 13 m. Find s and the area. On which measure will the grass be laid?
Model answer (board format)
s = 27 m. √[27×7×6×14] = √15876 = 126 square metres. The grass is laid on the area.
Check your answer:
6
The parallel sides of a trapezium roof are 8 m and 4 m, and the height is 3 m. Write the area of the waterproof layer.
Model answer (board format)
(1/2) × (8+4) × 3 = 18 square metres.
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
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🧠 What you learned + equation sheet
What you learned
- If the height is known, the area is (1/2) × base × height.
- s = (a + b + c) / 2 is the semi-perimeter.
- Heron area is the square root of s(s − a)(s − b)(s − c).
- On an equilateral side a the area also becomes (√3 / 4) a².
- One diagonal splits a quadrilateral into two triangles.
- A fence is on the perimeter, and grass or polish is on the area.
| What | Keep this |
|---|---|
| Base-height | (1/2) × b × h |
| Semi-perimeter | s = (a+b+c)/2 |
| Heron | √[s(s−a)(s−b)(s−c)] |
| Equilateral | (√3 / 4) a² |
| Quadrilateral | two triangles |
| Unit | m² or cm² |
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.