The area of an isosceles triangle each of whose equal side’s measures 13 cm and whose base measures 20 cm is ____ $c m 2$ .

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Detailed Solution

The area of an isosceles triangle each of whose equal side’s measures 13 cm and whose base measures 20 cm is 83.06

c m 2

.
Given an isosceles triangle each of whose equal side’s measures 13 cm and whose base measures 20 cm.
Drawing a median on base BC,
Question Image

Now,

B D = B C 2 ⇒ B D = 202 ⇒ B D = 10 c m

Using Pythagoras theorem in triangle ABC,

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 + 102 ⇒ A D 2 = 169 − 100 ⇒ A D 2 = 69 ⇒ A D = 69

Now, the area of triangle is

A = 12 × B a s e × H e i g h t ⇒ A = 12 × 20 × 69 ⇒ A = 1069 ⇒ A = 83.06 c m 2

The area of triangle is

83.06 c m 2

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