Question

In the figure, ABCD is a square of side 14 cm and a circle is inscribed in it. Find the area of the shaded part as shown in the figure

Answer 1

Answer:

29.75cm^2

Step-by-step explanation:

Side of square = 14cm = diameter of the circle inscribed in it.
∴Radius of the circle = 7cm.
Assuming the center of the circle to be 'O', joining the lines from center of the circle to vertex C and B of square.
Area of triangle BOC formed = (area of square/4) = (14*14)/2= 7*14= 98cm^2
Area of the part of circle present inside triangle COB = (theta /360) (pi) (r)^2
= (90/360) pi (7)^2 = (1/4)pi(49) = 22*7/4 = 38.5cm^2.
Now,
2(area of shaded region) = area of triangle - area of part of circle present in the triangle.
2(area of shaded region) = 98 - 38.5= 59.5cm^2

(area of shaded region) = (59.5cm^2)/2 = 29.75cm^2.

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