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