Question

find the area of an isosceles triangle whose equal sides are 12 cm and is the perimeter is 30cm

Answer 1

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First, we will find the third of this triangle.

Let the third side be X

Sum of all sides = perimeter of triangle
12 + 12 + X = 30
24 + X = 30
X = 30 - 24
X = 6 cm

Hence, the third side = 6 cm

Now we can find area.

Area of triangle
= 1/2 X b x h
= 1/2 X 6 X 12
= 1/2 X 72
= 36 cm²

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Answer 2

Given : length of equal side of triangle = 12 cm and its perimeter is 30 cm

Therefore, the third side of the triangle = 30-( 12 + 12 )

= 30 - 24

= 6cm

To find : The area

Solution

The semi perimeter of the triangle = 30 /2

= 15 cm

By using Heron's formula

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

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

$\implies \: Area = \sqrt{15 \times 3 \times 3 \times 9}$

$\implies \: Area = \sqrt{3 \times 5 \times 3 \times 3 \times 3 \times 3}$

$\implies \: Area = 3 \times 3 \sqrt{3 \times 5}$

$\large \bold{ \implies \: Area = 9 \sqrt{15} }$ Sq. cm