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An isosceles triangle has perimeter 30 cm and each of its equal sides is 12 cm. The area of the triangle is ____ $c m 2$ .

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Detailed Solution

An isosceles triangle has perimeter 30 cm and each of its equal sides is 12cm. The area of the triangle is 34.85

c m 2

.
Given an isosceles triangle has perimeter 30 cm and each of its equal sides is 12 cm.
Let the unknown side = x.
Perimeter of triangle is,= sum of all sides

30 = 12 + 12 + x ⇒ 30 − 12 − 12 = x ⇒ x = 6 c m

Now the value of semi-perimeter (s) is,

s = 302 ⇒ s = 15 c m

Area of triangle using Heron’s formula is,

A r e a = s (s − a) (s − b) (s − c) ⇒ A r e a = 15 × 15 − 12 × 15 − 12 × 15 − 6 ⇒ A r e a = 15 × 3 × 3 × 9 ⇒ A r e a = 1215 ⇒ A r e a = 915 c m 2 ⇒ A r e a = 34.85 c m 2

The area of triangle is 34.85

c m 2

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