Question

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

Answer 1

Let the unknown side of isosceles triangle be ' x ' cm.

We know that, two equal sides of isosceles triangle is 12 cm ( each ).

Perimeter of triangle = Sum of all three sides.

=> 30 = 12 + 12 + x

=> 30 = 24 + x

=> 30 - 24 = x

•°• x = 6

Three sides of the given triangle are -

• 6 cm ( a )
• 12 cm ( b )
• 12 cm ( c )

Semi - Perimeter = Perimeter/2

=> S = 6 + 12 + 12/2

=> S = 30/2

•°• S = 15 cm

We know that,

Area of triangle =

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

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

$\sf =\sqrt{15(9)(3)(3)}$

$\sf =\sqrt{3\times 5\times 3\times 3\times 3\times 3}$

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

Hence,

Area of the given triangle is $\sf 9\sqrt{15}\:cm^2$

$\rule{200}2$

Answer 2

☆ Solution ☆

Given :-

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

To Find :-

The area of the triangle.

Step-by-Step-Explaination :-

Let the third side be x

So,

12 + 12 + x = 30

24 + x = 30

x = 30 - 24

x = 6

Hence,

The length of the third side is 6 cm.

Now,

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

By using Heron's Formula,

As we know that :-

Area of triangle = √ s ( s - a ) ( s - b ) ( s- c )

Putting the respective value,

√ 15 ( 15 - 12 ) ( 15 - 12 ) ( 15 - 6 ) cm²

√ 15 × 3 × 3 × 9 cm²

9 √ 15 cm²

Hence Solved !