The adjacent figure consists of four half circles and two quarter circles. If OA = OB = OC = OD = 14 cm. Find the area of the shaded region.

Let the area of a semicircle be A_S and the area of a quadrant be A_Q

Since there are four semi-circles, out of which two are shaded and two are unshaded, therefore the area of shaded region is equal to:

Since the area of shaded region is equal on both sides of line AOB,

So, if we calculate area of upper portion, then we can simply twice that area in order to get required area.

In figure above, S1, S2, S3,and S4 represents semi-circles and Q1 and Q2 represents quadrants.

⇒ Area of shaded region = 2 × (area of upper shaded portion on line AOB)

⇒ Area of shaded region = 2 × [area(S1) + area(Q1) – area(S2)]

As S1 and S2 are equal because of same radius, therefore their area will also be equal i.e area(S1) = area(S2)

⇒ Area of shaded region = 2 × area(Q1)

⇒ Area (Q1) = 154 sq.cm

⇒ Required area = 2 × area(Q1)

⇒ 2 × 154 = 308 sq.cm

∴ Area of shaded region is 308 sq.cm