Percentage of the area shaded = 55%
Solution:
Perimeter of the square = 40 cm
Each side of the square =
= 10 cm
Area of the square = ![\text{side}^2](https://tex.z-dn.net/?f=%5Ctext%7Bside%7D%5E2)
= 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 =
![$=\frac{1}{2}\times 3\times 10](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%203%5Ctimes%2010)
Area of the smaller triangle = 15 cm²
Base of the larger triangle = 10 cm – 4 cm = 6 cm
Height of the larger triangle = 10 cm
Area of the larger triangle =
![$=\frac{1}{2}\times 6\times 10](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%206%5Ctimes%2010)
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 = ![\frac{\text{Area of the shaded portion}}{\text{Total area of the square}}\times100\%](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BArea%20of%20the%20shaded%20portion%7D%7D%7B%5Ctext%7BTotal%20area%20of%20the%20square%7D%7D%5Ctimes100%5C%25)
![$=\frac{55}{100}\times100\%](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B55%7D%7B100%7D%5Ctimes100%5C%25)
Percentage of the area shaded = 55%