Question

ABC is an isosceles triangle with AB = AC = 12 cm and BC = 8 cm. The area of the triangle is ______.

Options

• `32sqrt{2}" cm"^2`

• `16sqrt{2}" cm"^2`

• `8sqrt{2}" cm"^2`

• `12sqrt{2}" cm"^2`

Answer 1

ABC is an isosceles triangle with AB = AC = 12 cm and BC = 8 cm. The area of the triangle is `bbunderline(32sqrt{2}" cm"^2)`.

Explanation:

The height (altitude) AD to the base BC bisects it into segments of 4 cm.

Using Pythagoras’ theorem,

AD = `sqrt{12^2 - 4^2} = sqrt{128} = 8sqrt{2}" cm"`,

giving an area of `1/2 xx 8 xx 8sqrt{2} = 32sqrt{2}" cm"^2`.