In figure, find the area of the shaded region, if ABCD is rectangle with AB =80 cm and BC = 70 cm. Angle AED =90and DE =42 cm and a semicircle is drawn with BC as a diameter.
Answers
Answer:
2499
Step-by-step explanation:
Given In figure, find the area of the shaded region, if ABCD is rectangle with AB =80 cm and BC = 70 cm. Angle AED =90 and DE =42 cm and a semicircle is drawn with BC as a diameter.
We know Area of rectangle = length x breadth
= 80 x 70 = 5600 sq cm
Radius of semi circle = 70 /2 = 35 cm
So area is given by π r^2 / 2
= 22/7 x 35 x 35 / 2
= 35 x 55 = 1925 sq cm
Now by pythagoras theorem we have
AD^2 = DE^2 + AE^2
70^2 = 42^2 + h^2
4900 = 1764 + h^2
h^2 = 3136
h = 56 cm
Now area of triangle = 1/2 x b x h
= 1/2 x 42 x 56
= 1176 sq cm
So area of shaded region = area of rectangle - (area of triangle + area of semi-circle)
= 5600 - (1925 + 1176) = 2499 sq cm
Area will be 2499 sq cm
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