Question

In an isosceles triangle, the unequal side is 22 cm and perimeter is 144 cm. Find its area.

Answer 1

Given:

• Isosceles triangle with unequal side (base) = 22 cm
• Perimeter of triangle = 144 cm

Stepwise calculation:

1. Let the equal sides of the triangle be each of length a cm. 

Since the perimeter is sum of all sides,

2a + 22 = 144

⇒ 2a = 144 – 22 = 122

⇒ `a = 122/2`

⇒ a = 61 cm

2. The height h of the triangle dropping on the base 22 cm bisects it, so half of base is `22/2` = 11 cm.

3. Use Pythagoras theorem to find height h:

`h = sqrt(a^2 - (b/2)^2)`

= `sqrt(61^2 - 11^2)`

= `sqrt(3721 - 121)`

= `sqrt(3600)`

= 60 cm

4. Area of the isosceles triangle:

A = `1/2` × base × height

= `1/2 xx 22 xx 60`

= 660 cm²

The area of the isosceles triangle is 660 cm².