7. ABCD is a square of side 14 cm. With centers A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.
Solution:
Area of shaded portion= Area of square- Area of four sectors (1)
Area of square = side x side = 14 x 14=196
(2)
Side of square =14 cm which means that radius of circle
cm
Area of 1 sector
Area of 4 sectors
(3)
Putting (2) and (3) in (1), we get
Area of shaded portion=196-154=42
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