Percentage of the area shaded = 55%
Solution:
Perimeter of the square = 40 cm
Each side of the square = [tex]\frac{40}{4}[/tex] = 10 cm
Area of the square = [tex]\text{side}^2[/tex]
= 10²
= 100
Total area of the square = 100 cm²
The unshaded portion is two triangles.
Base of the smaller triangle = 10 cm – 7 cm = 3 cm
Height of the smaller triangle = 10 cm
Area of the smaller triangle = [tex]\frac{1}{2}\times \text{base}\times \text{height}[/tex]
[tex]$=\frac{1}{2}\times 3\times 10[/tex]
Area of the smaller triangle = 15 cm²
Base of the larger triangle = 10 cm – 4 cm = 6 cm
Height of the larger triangle = 10 cm
Area of the larger triangle = [tex]\frac{1}{2}\times \text{base}\times \text{height}[/tex]
[tex]$=\frac{1}{2}\times 6\times 10[/tex]
Area of the larger triangle = 30 cm²
Area of the shaded portion = Area of the square – Area of the smaller
triangle – Area of the larger triangle
= 100 cm² – 15 cm² – 30 cm²
Area of the shaded portion = 55 cm²
Percentage of the area shaded = [tex]\frac{\text{Area of the shaded portion}}{\text{Total area of the square}}\times100\%[/tex]
[tex]$=\frac{55}{100}\times100\%[/tex]
Percentage of the area shaded = 55%
