Question

Do you know how to do this question

Answer 1

Percentage of the area shaded = 55%

Solution:

Perimeter of the square = 40 cm

Each side of the square =
`(40)/(4)` = 10 cm

Area of the square =
`\text{side}^2`

= 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 =
`(1)/(2)* \text{base}* \text{height}`

`$=(1)/(2)* 3* 10`

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 =
`(1)/(2)* \text{base}* \text{height}`

`$=(1)/(2)* 6* 10`

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}}*100\%`

`$=(55)/(100)*100\%`

Percentage of the area shaded = 55%