Find the perimeter and area of the shaded region in the given figure.

Question

KnowledgeBoat · Accepted Answer

Given, AB = 12 cm BC = 16 cm AC is the diameter of the semicircle. Angle in a semicircle is a right angle, thus, ABC = 90 Using Pythagoras theorem in △ABC: ⇒ AC2 = AB2 + BC2 ⇒ AC2 = 122 + 162 ⇒ AC2 = 144 + 256 ⇒ AC2 = 400 ⇒ AC = = 20 cm. So, radius = = 10 cm. Semicircle arc = πr = 3.14 × 10 = 31.4 cm Perimeter = Semicircle arc + side AB + side BC Perimeter = 31.4 + 12 + 16 = 59.4 cm Area of shaded region = Area of semicircle - Area of triangle Calculating the area of semicircle, Area of triangle = × AB × BC = × 12 × 16 = 6 × 16 = 96 cm2. Area of shaded region = 157 - 96 = 61 cm2. Hence, perimeter of shaded region = 59.4 cm and area of shaded region = 61 cm2.

Mathematics

Find the perimeter and area of the shaded region in the given figure.

Mensuration

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