In the given figure, AB = , where BC = 14 cm. Find : (i) Area of quad. AEFD (ii) Area of △ABC (iii) Area of semicircle. Hence, find the area of shaded region.

Question

KnowledgeBoat · Accepted Answer

Given, BC = 14 cm AB = × 14 = 7 cm. BC is a diameter of the semicircle So, radius = × 14 = 7 cm. (i) Area of quadrilateral AEFD: Height (AE) = AB + BE = 7 + 7 = 14 cm. Width : AD = BC = 14 Area of quad. AEFD = 14 × 14 = 196 cm2. Hence, area of quad. AEFD = 196 cm2. (ii) Area of △ABC: Area = × base × height = × BC × AB = × 14 × 7 = 7 × 7 = 49 cm2. Hence area of △ABC = 49 cm2. (iii) Calculating, Hence, area of semicircle = 77 cm2. Area of shaded region = Area of quad. AEFD - (Area of triangle ABC + Area of semicircle) = 196 - (49 + 77) = 196 - 126 = 70 cm2. Hence, area of shaded region = 70 cm2.

Mathematics

In the given figure, AB = , where BC = 14 cm. Find : (i) Area of quad. AEFD (ii) Area of △ABC (iii) Area of semicircle. Hence, find the area of shaded region.

Mensuration

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