Answer : The area of the shaded portion is 33.72 yd².
Step-by-step explanation :
Given:
Length of the box = 10 yd
Width of the box = 4 yd
Area of the shaded portion = Area of rectangular box - Area of half circle
First we have to calculate the area of rectangular box.
Area of rectangular box = Length of the box × Width of the box
Area of rectangular box = 10 yd × 4 yd
Area of rectangular box = 40 yd²
Now we have to calculate the area of half circle.
As we know that:
Area of circle = π × r²
where,
r = radius of circle
Area of half circle = [tex]\frac{\pi \times r^2}{2}[/tex]
Radius of circle = [tex]\frac{4yd}{2}=2yd[/tex]
Area of half circle = [tex]\frac{3.14 \times (2yd)^2}{2}[/tex]
Area of half circle = 6.28 yd²
Now we have to calculate the area of the shaded portion.
Area of the shaded portion = Area of rectangular box - Area of half circle
Area of the shaded portion = 40 yd² - 6.28 yd²
Area of the shaded portion = 33.72 yd²
Therefore, the area of the shaded portion is 33.72 yd².
