Question

An isoscels triangle perimeter 30 cm and each of equal side is 12cm . find the area of tiangle?

Answer 1

HERE IS YOUR ANSWER :

Peimeter : 30 cm

Lenght of equal side : 12 cm

Let lenght of third side be x
Then,

x +12 + 12 = 30
x + 24 = 30
x = 6 cm

The area of isosceles triangle = 1/4 a root 4b^2 - a^2

= 1/4 × 6 root 4 × 12 × 12 - 6 × 6
= 3 / 2 root 576 - 36
= 3 / 2 × 23.23
= 34.85

Thus area of given isosceles triangle is approx. equal to 34.85 cm^2

Answer 2

First,let the third side be x.

It is given that the length of the equal sides us 12 cm and it's perimeter is 30 cm.

So,$30=12+12+x$

$⇒ 30 = 24 + x$

$⇒24 + x = 30$

$⇒ x= 30 - 24$

$⇒ x = 6$

So,the length of the third side is 6 cm.

Thus,the semi perimeter of the isosceles triangle (s) = 30/2 cm =15 cm

By using Heron's Formula,

Area of the triangle,

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

$= \sqrt{15(15 - 12)(15 - 12)(15 - 6)} \: {cm}^{2}$

$= \sqrt{15 \times 3 \times 3 \times 9} \: {cm}^{2}$

$= 9 \sqrt{15} \: {cm}^{2}$