BECE Mathematics 2023 Paper

Concept:The shaded portion is the area inside the square but outside the inscribed circle.So, shaded area $=$ Area of square $-$ Area of circle.Explanation:Side of the square $=2\ \mathrm{cm}$.Area of square $=2\ \mathrm{cm}\times 2\ \mathrm{cm}=4\ \mathrm{cm}^2$.The circle is inscribed in the square, so its diameter equals the side of the square.Diameter $=2\ \mathrm{cm}$, hence radius $r=\frac{2}{2}=1\ \mathrm{cm}$.Area of circle $=\pi r^2=\frac{22}{7}\times (1)^2=\frac{22}{7}\approx 3.14\ \mathrm{cm}^2$.Shaded area $=4\ \mathrm{cm}^2-3.14\ \mathrm{cm}^2=0.86\ \mathrm{cm}^2$.Answer:The area of the shaded portion is $0.86\ \mathrm{cm}^2$.Correct option: A.