The ratio of the area of the shaded portion to the area of the unshaded
portion is given by the ratio of their numbers in the large square.
- The area of the shaded portion = 1.5 ft.²
Reasons:
The description of the figure is as follows;
The larger square is divided into a number of smaller square
The side length of the larger square = 2 ft.
The number of shaded square = 6
The number of plain squares = 10
Required:
The area of the shaded portion.
Solution:
The ratio of the area of the shaded to the unshaded portion is; 6 : 10 = 3 : 5
Therefore;
[tex]\displaystyle Area \ of \ the \ shaded \ portion = \frac{3}{3 + 5} \times Area \ of \ the \ square = \mathbf{\frac{3}{8} \times Area \ of \ the \ square}[/tex]
Area of the square, A = Side × Side = Side²
∴ A = 2 ft. × 2 ft. = 4 ft.²
Area of the square, A = 4 ft.²
[tex]\displaystyle Area \ of \ the \ shaded \ portion = \frac{3}{8} \times 4 \ ft.^2 = \frac{3}{2} \ ft.^2 = 1.5 \ ft.^2[/tex]
The area of the shaded portion = 1.5 ft.².
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