Question

An isoceles triangle has a perimeter 30cm and each of the equal side is 12 cm .find the area of ihe triangle

Answer 1

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 cm

Answer 2

Let the third side be x

Perimeter of the triangle = 12+12+x = 30

24+x = 30

x = 6cm

The Area of the Triangle Using Herons Formula =$\sqrt{s(s-a)(s-b)(s-c)}$

s= a+b+c/2 = 12+12+6/2 = 30/2 = 15

= $\sqrt{15(15-12)(15-12)(15-6)}$

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

=  $\sqrt{1215}$

 = 34.85cm²

Therefore, Area of triangle = 34.85cm²

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