in the figure given below, ABCD is a square of side 14 cm with E. F. G and H as the midpoint of sides AB, BC, CD, and, DA respectively. The area of the shaded portion is
Answers
Given : ABCD is a square of side 14 cm with E. F. G and H as the midpoint of sides AB, BC, CD, and, DA respectively.
To Find : The area of the shaded portion
Solution:
AB + BC = CD = AD = 14 cm
AH = DH = AE = BE = DG = CG = BF = CF = 14/2 = 7 cm
HF = 14 cm
The area of the shaded portion = Area of semicircle with diameter HF (14 cm) + Area of rectangle DCFH - Area of sector DGH - area of sector CGF
Area of semicircle with diameter HF (14 cm)
radius = 14/2 = 7 cm
Area = (1/2)π(7)² = (1/2) (22/7) (7)² = 77 cm²
Area of rectangle DCFH = 14 * 7 = 98 cm²
Area of Sector DGH = (90/360)π(7)² = 77/2 cm²
Area of Sector CGF = (90/360)π(7)² = 77/2 cm²
The area of the shaded portion = 77 + 98 - 77/2 - 77/2
= 98 cm²
The area of the shaded portion is 98 cm² .
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