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

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9 \sqrt{15} {cm}^{2}

8 \sqrt{15} {cm}^{2}

7 \sqrt{15} {cm}^{2}

6 \sqrt{15} {cm}^{2}

answer is A.

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Detailed Solution

Given,
Perimeter of isosceles triangle = 30 cm
Length of equal sides = 12 cm
Assume that
The third side of triangle =

x cm

As, perimeter is the sum of all three sides. So,

x + 12 + 12 = 30

x + 24 = 30

x = 30 - 24

x = 6

Therefore,
Third side of triangle = 6 cm
Using Heron's formula
Area of triangle

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

Where,

s = \frac{a + b + c}{2}

s = \frac{30}{2} = 15

Now calculate the area of triangle

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

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

= 3 \times 3 \times \sqrt{15} {cm}^{2}

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

Hence, the area of the triangle

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

Correct option is 1.

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