Each of the equal sides of an isosceles triangle is 13 cm and base is 24 cm. The area of the triangle is ____ $c m 2$ .

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Detailed Solution

Each of the equal sides of an isosceles triangle is 13 cm and base is 24 cm. The area of the triangle is 60

c m 2

.
Given each of the equal sides of an isosceles triangle is 13 cm and base is 24 cm.
Drawing a median on base BC,
Question Image

As median divides the side into two equal parts, so BD=12cm
Using Pythagoras theorem in triangle ABD,

H y p o t e n u s e 2 = B a s e 2 + H e i g h t 2

A B 2 = A D 2 + B D 2 ⇒ 132 = A D 2 + 122 ⇒ 169 = A D 2 + 144 ⇒ A D 2 = 25 ⇒ A D = 5

Now, the area is

A = 12 × b × h ⇒ A = 12 × 24 × 5 ⇒ A = 60 c m 2

Area of triangle is 60

cm 2

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