In the given figure, ABCP is a quadrant of a circle of radius 14 cm. With AC as diameter, a semi-circle is drawn. Find the area of shaded region.
Mensuration
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Question

In the given figure, ABCP is a quadrant of a circle of radius 14 cm. With AC as diameter, a semi-circle is drawn. Find the area of shaded region.

KnowledgeBoat · Accepted Answer

Given, ABCP is a quadrant of radius = 14 cm AB = BC = 14 cm AC is the diameter of semicircle. Using Pythagoras theorem in △ABC, ⇒ AC2 = AB2 + BC2 ⇒ AC2 = 142 + 142 ⇒ AC2 = 196 + 196 ⇒ AC2 = 392 ⇒ AC = cm. So, radius of semicircle = cm. Calculating area of semicircle : Calculating area of quadrant : Calculating area of triangle : Area of triangle ABC = × AB × BC = × 14 × 14 = 7 × 14 = 98 cm2. Shaded area = (Area of semicircle AQC) - [(Area of quadrant APCB) - (Area of triangle ABC)] Area of shaded region = 154 - [(154 - 98)] = 154 - 56 = 98 cm2. Hence, area of shaded region = 98 cm2.

Mathematics

In the given figure, ABCP is a quadrant of a circle of radius 14 cm. With AC as diameter, a semi-circle is drawn. Find the area of shaded region.

Mensuration

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