Find the area of a triangle, given that its sides are 8 cm and 11 cm long, and its perimeter is 32 cm. Class 9

Find the area of a triangle, given that its sides are 8 cm and 11 cm long, and its perimeter is 32 cm. Class 9

Question 1.

Find the area of a triangle, given that its sides are 8 cm and 11 cm long, and its perimeter is 32 cm. Class 9

Solution:

Sides of triangle are

a = 8 cm, b = 11 cm

Perimeter = 32 cm

∴ a + b + c = 32 cm

8 + 11 + c = 32 cm

∴ c = 32 - 8 - 11

c = 13 cm

Semi-perimeter(s) = $\frac{32}{2}$ = 16

Area of triangle by Heron's formula

$\begin{aligned} & =\sqrt{s(s-a)(s-b)(s-c)} \\ & =\sqrt{16(16-8)(16-11)(16-13)} \\ & =\sqrt{16 \times 8 \times 5 \times 3} \\ & =\sqrt{16 \times 120} \\ & =\sqrt{1920} \\ & =\sqrt{64 \times 30} \\ & =8 \sqrt{30}\end{aligned}$

∴ Area of triangle = $8 \sqrt{30}$ cm²