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 = $\frac{40}{4}$ = 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 = $\frac{1}{2}\times \text{base}\times \text{height}$

                                              $=\frac{1}{2}\times 3\times 10$

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 = $\frac{1}{2}\times \text{base}\times \text{height}$

                                              $=\frac{1}{2}\times 6\times 10$

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 = $\frac{\text{Area of the shaded portion}}{\text{Total area of the square}}\times100\%$

                                                    $=\frac{55}{100}\times100\%$

Percentage of the area shaded = 55%