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
