Question

An isosceles triangle has a perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

Answer 1

Equal sides: a = b = 12 cm (given)

The formula for the perimeter of a triangle:
Perimeter(P) = a + b + c

30 = 12 + 12 + c (Given, perimeter = 30 cm)

c = 30 - 24

c = 6 cm

Now, Semi Perimeter (s) $=\frac{a+b+c}{2}=15$ cm

Area of a triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{15(15-12)(15-12)(15-6)}$

$=\sqrt{15\times 3\times 3\times 9}$

$=\sqrt{1215}$

$=9\sqrt{15}c{m}^2$

Area of the triangle $=9\sqrt{15}c{m}^2$