Question

The given figure shows a right-angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.

Answer 1

From ΔABC,

AB = `sqrt("AC"^2 - "BC"^2)`

= `sqrt( 16^2 - 8^2)`

= `sqrt192`

Area of ΔABC

ΔABC = `1/2 xx 8 xx sqrt192`

= `4 sqrt192` 

Area of ΔBCD

ΔBCD = `sqrt3/4 xx 8^2`

= `16 sqrt3`

Now

ABD = ABC - BDC

= `4sqrt192 - 16sqrt3`

= `32sqrt3 - 16sqrt3`   

= `16sqrt3` sq.cm