Question

 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. 

Answer 1

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  

Answer 2

Hey, mate

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