Divya Ryan's answer to Kc's Primary 6 Maths Geometry Singapore question.
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Since F and E are the centers of the two semicircles, they are the centers of AD and DC.
Therefore, AF = FD = DE = EC = 12 / 2 = 6cm
This means the radii of the two semicircles = 6cm
Area of the shaded portion = Area of ABCD - Area of FGED - Area of quadrant AGF - Area of quadrant GCE = 12 * 12 - 6 * 6 - 1/4 πr^2 - 1/4 πr^2 = 108 - 2 * 1/4 π * 6^2 = 51.5 cm^2 (1 decimal place)
CG = GA = 1/4 * 2 πr = 1/4 * 2 π * 6 = 3 π
Perimeter of the shaded region = AB + BC + CG + GA = 12 + 12 + 3 π + 3 π = 42.8cm (1 decimal place)
Therefore, AF = FD = DE = EC = 12 / 2 = 6cm
This means the radii of the two semicircles = 6cm
Area of the shaded portion = Area of ABCD - Area of FGED - Area of quadrant AGF - Area of quadrant GCE = 12 * 12 - 6 * 6 - 1/4 πr^2 - 1/4 πr^2 = 108 - 2 * 1/4 π * 6^2 = 51.5 cm^2 (1 decimal place)
CG = GA = 1/4 * 2 πr = 1/4 * 2 π * 6 = 3 π
Perimeter of the shaded region = AB + BC + CG + GA = 12 + 12 + 3 π + 3 π = 42.8cm (1 decimal place)
Date Posted:
4 years ago
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