Question

Find the area of the shaded figure ?
In the attachment..
(cm)

Answer 1

In the question,

     Length of rectangle = 20 cm

     Breadth of rectangle = 10 cm

Area of the rectangle = length × breadth

                               = 20 cm × 10 cm

                               = 200 cm^2

If we notice, the part which is not included in the rectangle is a triangle. and the third side which is not given is equal to the breadth of the rectangle i.e. 10 cm, therefore the third side of the triangle is 10 cm. As 6 , 8 and 10 are Pythagorean triplets, the excluded part of the rectangle is a right angled triangle and right angle is between the given sides 6 and 8.

Therefore,

Area of excluded part = $\dfrac{1}{2}\times base \times height$

           

                       = 1 / 2 × 6 × 8 cm^2

                       = 6 × 4 cm^2

                       = 24 cm^2

And included part is a semi - circle, and the radius of the semicircle is the half of the breadth of the rectangle. Radius of that circle: ( 10 cm / 2 ) = 5 cm

Area of semi circle = πr^2 / 2

                       = $\dfrac{3.14 \times (5cm)^{2}}{2}$

                       = 39.25 cm^2

Therefore,

Area of shaded region = area of rectangle - area of excluded part + area of included part

Area of the shaded region = 200 cm^2 - 24 cm^2 + 39.25 cm^2

Area of shaded region = 215.25 cm^2