Question

Find the area of an isosceles triangle each of whose equal sides is 13 cm and whose base is 24 cm.

Answer 1

Given: Each equal side a = 13 cm, base b = 24 cm.

Step-wise calculation:

1. Draw the altitude from the apex to the base; it bisects the base.

So half-base = `24/2` = 12 cm.

2. Height `h = sqrt(a^2 - ("half-base")^2)`

= `sqrt(13^2 - 12^2)`

= `sqrt(169 - 144)`

= `sqrt(25)`

= 5 cm

3. Area = `1/2 xx "base" xx "height"`

= `1/2 xx 24 xx 5`

= 12 × 5

= 60 cm²

Area of the isosceles triangle = 60 cm².