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CBSE · Class 9 · Mathematics

Measuring Space: Perimeter and Area

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
The semi-perimeter of a triangle with sides 15 cm, 36 cm and 39 cm is:
  1. 46 cm
  2. 90 cm
  3. 39 cm
  4. 45 cm
2.
The area of a triangle with sides 64 cm, 100 cm and 156 cm is:
  1. 3,840 cm2
  2. 3,200 cm2
  3. 1,920 cm2
  4. 320 cm2
3.
The area of an equilateral triangle of side 20 cm is:
  1. 100 cm2
  2. 200√3 cm2
  3. 60√3 cm2
  4. 100√3 cm2
4.
The sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 108 cm. Its area is:
  1. 6 cm2
  2. 972 cm2
  3. 108 cm2
  4. 486 cm2
5.
In Heron's formula, s stands for:
  1. the area
  2. the longest side
  3. half the perimeter
  4. the perimeter
6.
An isosceles triangle has equal sides of 30 cm and a base of 48 cm. Its area is:
  1. 480 cm2
  2. 432 cm2
  3. 1,440 cm2
  4. 864 cm2
7.
For a triangle with sides 10 cm, 17 cm and 21 cm, s(s − a)(s − b)(s − c) equals:
  1. 7,056
  2. 14,112
  3. 84
  4. 168
8.
Assertion (A): The area of a triangle with sides 27 cm, 30 cm and 51 cm is 324 cm2.
Reason (R): By Heron's formula, area = √(s(s − a)(s − b)(s − c)), where s is the semi-perimeter.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
Find the area of a triangle with sides 36 cm, 51 cm and 75 cm.
10.
A rhombus has sides of 20 cm and one diagonal of 24 cm. Find its area.
11.
The perimeter of an equilateral triangle is 24 cm. Find its area.
12.
A triangular wall has sides 21 m, 72 m and 75 m. Find the cost of painting it at Rs 19 per m2.
13.
A triangle has a perimeter of 50 cm. Two of its sides are 16 cm and 17 cm. Find its area.
14.
A triangle has sides 80 cm, 84 cm and 116 cm. Find the height on its longest side.
15.
An isosceles triangle has a perimeter of 150 cm and a base of 72 cm. Find its area.
16.
A parallelogram has sides of 26 cm and 40 cm, and one diagonal of 42 cm. Find its area.
Section C — Word problems4 × 4 = 16 marks
17.
A triangular park has sides 32 m, 50 m and 78 m. Find its area, and the cost of planting grass at Rs 18 per m2.
18.
A traffic signboard is an equilateral triangle with sides of 42 cm. Find its area.
19.
An umbrella is made of 12 triangular pieces of cloth, each with sides 5 cm, 5 cm and 6 cm. How much cloth is used?
20.
A field ABCD has AB = 9 m, BC = 10 m, CD = 16 m, DA = 17 m and diagonal AC = 17 m. Find its area.
AmbifulWorksheets
Practice that never repeats
CBSE · Class 9 · Mathematics

Answer key

Measuring Space: Perimeter and Area · AW-9M-HER-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) 45 cm(15 + 36 + 39) ÷ 2 = 45
2(c) 1,920 cm2s = 160; √(s(s − a)(s − b)(s − c)) = 1,920
3(d) 100√3 cm2(√3/4) × 202 = 100√3
4(d) 486 cm2sides 27, 36, 45; area 486
5(c) half the perimeter—
6(b) 432 cm2s = 54; area = 432
7(a) 7,056it is the square of the area: 842 = 7,056
8(a) Both A and R are true, and R is the correct explanation of A.A is true: s = 54 and Heron's formula gives 324. R is true and explains A.
9810 cm2s = 81; √(81 × 45 × 30 × 6) = 810
10384 cm2the diagonal makes two triangles with sides 20, 20, 24, each 192 cm2
1116√3 cm2side = 8; (√3/4) × 82 = 16√3
12Rs 14,364area = 756 m2; 756 × 19 = 14,364
13120 cm2third side = 50 − 16 − 17 = 17; area = 120
141680/29 cmarea = 3,360; height = 2 × 3,360 ÷ 116 = 1680/29
15540 cm2equal sides = (150 − 72) ÷ 2 = 39; area = 540
161,008 cm2the diagonal makes two equal triangles of 504 cm2
17480 m2; Rs 8,640s = 80; area = 480; × 18 = 8,640
18441√3 cm2(√3/4) × 422 = 441√3
19144 cm2one piece = 12 cm2; × 12 = 144
20156 m2△ABC = 36, △ACD = 120; total 156