MATH SOLVE

3 months ago

Q:
# Find the area of the shaded portion in the square.(assuming the central point of each arc is the corresponding corner)

Accepted Solution

A:

Answer:The area of the shaded = 8 - 2π units²Step-by-step explanation:The area of the shaded portion = area square - area not shaded portionNot 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