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Question
In the given figure, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside' the region. Find the area of the shaded region. [Use π = 3.14]
Solution
In right triangle AED
AD2 = AE2 + DE2
= (9)2 + (12)2
= 81 + 144
= 225
∴ AD2 = 225
⇒ AD = 15 cm
We know that the opposite sides of a rectangle are equal
AD = BC = 15 cm
= Area of the shaded region = Area of rectangle − Area of triangle AED + Area of semicircle
`="AB"xx"BC" - 1/2xx"AE"xx"DE"+1/2pi("BC"/2)^2`
`= 20xx15-1/2xx9xx12+1/2xx3.14(15/2) `^2
= 300 - 54 + 88.31
= 334. 31 cm2
Hence, the area of shaded region is 334.31 cm2
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