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Question
Find the area of the unshaded region
Solution
Since ABD is a right angle triangle
AB2 = AD2 + BD2
= 122 + 162
= 144 + 256
= 400
AB = `sqrt(400)`
= 20 cm
Area of the right angle triangle = `1/2` bh sq.unit
= `1/2 xx 12 xx 16 "cm"^2`
= 6 × 16 cm2
= 96 cm2
To find the Area of the triangle ABC
Here a = 42 cm, b = 34 cm, c = 20 cm
s = `("a" + "b" + "c")/2`
= `(42 + 34 + 20)/2 "cm"`
= `96/2`
= 48 cm
s – a = 48 – 42 = 6 cm
s – b = 48 – 34 = 14 m
s – c = 48 – 20 = 28 m
Area of triangle
= `sqrt("s"("s" - "a")("s" - "b")("s" - "c"))`
= `sqrt(48 xx 6 xx 14 xx 28)`
= `sqrt(2^4 xx 3 xx 2 xx 3 xx 2 xx 7 xx 2^2 xx 7)`
= `sqrt(2^8 xx 3^2 xx 7^2)`
= 16 × 3 × 7 cm2
= 336 cm2
Area of the unshaded region = Area of the ΔABC – Area of the ΔABD
= (336 – 96) cm2
= 240 cm2
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