Question

Find the area of an isosceles triangle in which base is 12 cm and each of equal sides is 10 cm.

Answer 1

Given: Base = 12 cm, each equal side = 10 cm.

Step-wise calculation:

1. Drop the altitude from the apex to the midpoint of the base; it bisects the base into two segments of length 6 cm. This produces a right triangle with hypotenuse 10 cm and base 6 cm.

2. Height h = `sqrt(10^2 - 6^2)`

= `sqrt(100 - 36)`

= `sqrt(64)`

= 8 cm

3. Area = `1/2` × base × height 

= `1/2 xx 12 xx 8`

= 48 cm²

Equivalent isosceles-area formula:

`a/4 xx sqrt(4b^2 - a^2)`

Area = 48 cm².