Question

Find the area of the shaded portion in the square.

Answer 1

Answer:

The area of the shaded = 8 - 2π units²

Step-by-step explanation:

The area of the shaded portion = area square - area not shaded portion

Not shaded portion consists of two equal segments

∵ The side of the square = the radius of the circle = 2

∵ The measure of each angle of the square = π/2 (90° = π/2 rad)

∵ Area each segment = Area sector - area triangle

∵ Area triangle = 1/2 × (2) × (2) = 2 units²

∵ Area sector = (1/2)r²Ф ⇒ r = 2 , Ф = π/2

∴ Area sector = (1/2) (2)² (π/2) = π units²

∴ Area each segment = π - 2

∴ Area not shaded = 2(π - 2) = 2π - 4 units² ⇒ two segment

∵ Area square = 2 × 2 = 4 units²

∴ Area shaded portion = 4 - (2π - 4) = 4 - 2π + 4

                                      = 8 - 2π units²