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प्रश्न
In the given figure, ABCD is a rectangle with AB = 80 cm and BC = 70 cm, ∠AED = 90° and DE = 42 cm. A semicircle is drawn, taking BC as diameter. Find the area of the shaded region.
उत्तर
We know that the opposite sides of a rectangle are equal
AD = BC = 70 cm
In right triangle AED
AE2 = AD2 − DE2
= (70)2 − (42)2
= 4900 − 1764
= 3136
∴ AE2 = 3136
⇒ AE = 56
= 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]`
`= 80xx70-[1/2xx56xx42+1/2xx22/7(70/2)^2]`
= 5600 - 3101
= 2499 cm2
Hence, the area of shaded region is 2499 cm2
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