Question

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

Answer 1

Let The Third Side Be xcm.

Now Perimeter = 12+12+x

24+x = 30

x = 6

Now Find The Area Using Herons Formula

Semiperimeter = 30/2 = 15

Sq Root(15(15-12)(15-12)(15-6) ) = Sq Root(15*3*3*9) = Sq Root(1215) = 34.85 cm^2

So Area is 34.85cm^2

Answer 2

SOLUTION
Length of the equal sides = 12cm
Perimeter of the triangle = 30cm
Length of the third side = 30 - (12+12) cm = 6cm
Semi perimeter of the triangle(s) = 30/2 cm = 15cm
Using heron's formula,
Area of the triangle = √s (s-a) (s-b) (s-c)
                                       = √15(15 - 12) (15 - 12) (15 - 6)cm2
                                       = √15 × 3 × 3 × 9 cm2
                                       = 9√15 cm2