Class 9 Heron's Formula — practice questions with answers

Mensuration · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. What is the semi-perimeter of a triangle with sides 5 cm, 12 cm, and 13 cm?

Show answer

Answer: A) 15 cm

The semi-perimeter is calculated as

s = \frac{5 + 12 + 13}{2} = 15

2. Write Heron's formula for the area of a triangle whose sides are a, b, c and whose semi-perimeter is s.

Show answer

Answer: A) Area =

s (s - a) (s - b) (s - c)

Heron's formula states Area =

s (s - a) (s - b) (s - c)

, where

s = \frac{a + b + c}{2}

is the semi-perimeter.

3. The semi-perimeter of a triangle is 18 cm and two of its sides are 10 cm and 14 cm. What is the third side?

Show answer

Answer: A) 12

Perimeter = 2s = 36 cm. Third side = 36 - 10 - 14 = 12 cm.

4. Find the area of the triangular plot with sides 40 m, 24 m, and 32 m from the previous question.

Show answer

Answer: A) 384 m²

s = \frac{40 + 24 + 32}{2} = 48

. Area =

48 \times 8 \times 24 \times 16 = 147456 = 384

m².

5. A triangle has sides 35 cm, 54 cm, and 61 cm. Find its area.

Show answer

Answer: A)

4205

cm²

s = 75. Area =

75 (75 - 35) (75 - 54) (75 - 61) = 75 \times 40 \times 21 \times 14 = 882000

. Factoring:

882000 = 2^{4} \times 3^{2} \times 5^{3} \times 7^{2}

, so

882000 = 4 \times 3 \times 7 \times 5^{3} = 4 \times 3 \times 7 \times 5 \times 5 = 4205

cm².

10 free questions a day without an account — unlimited with a free account.