Question

Q-12 If the perimeter of a triangle is 32 cm and the sides are 8 cm and 11 cm, find its area.​

Answer 1

Answer:

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Answer 2

Given: Perimeter of a triangle = 32 cm

           Two sides of the triangle are 8 cm ($a$) and 11 cm ($b$)

To find: Area of the triangle

Let: Third side be $c$

Solution: According to the given question:

Perimeter of triangle = 32 cm

Two sides are 8 cm and 11 cm

∵ Perimeter of triangle = Sum of sides

⇒ $32 = 8 + 11 + c$

⇒ $c = 32 - 8 - 11$

⇒ $c = 13$

∵ Area of scalene triangle = $\sqrt{s(s-a)(s-b)(s-c)}$, where s is the semi-perimeter.

∵ $S = \frac{a \ + \ b\ +\ c}{2}$  [a, b and c are sides of triangle, $a + b + c$ = perimeter of triangle (32)]  

⇒ $S = \frac{8\ +\ 11\ +\ 13}{2} = \frac{32}{2} = 16$

Area of triangle = $\sqrt{16(16-8)(16-11)(16-13)}$

                          $= \sqrt{16(8)(5)(3)}$

                          $= \sqrt{1920}$ $= 43.81$ (ignoring negative value)

Hence, area of the triangle is $44 cm^{2}$ (approx.)