Question

In the figure, assume that angles that appear to be right angles are right angles. What is the area of the figure? use 3.14 for . 71.13 113.13 144.58 116.26

Answer 1

Option A:

The area of the figure is 71.13 square units.

Solution:

The figure is splitted into two shapes.

One is semi-circle and the other is trapezoid.

Radius of the semi-circle = 3

Area of the semi-circle = $\frac{1}{2}\pi r^2$

                                      $=\frac{1}{2} \times 3.14 \times 3^2$

Area of the semi-circle = 14.13 square units

Top base of the trapezoid = 8

Bottom base of the trapezoid = 11

Height of the trapezoid = 6

Area of the trapezoid = $\frac{1}{2}\times\text{sum of the parallel sides}\times\text{Height}$

                                    $=\frac{1}{2}\times{(8+11)}\times{6}$

                                    $=\frac{1}{2}\times{19}\times{6}$

Area of the trapezoid= 57 square units

Area of the figure = Area of the semi-circle + Area of the trapezoid

                              = 14.13 square units + 57 square units

                              = 71.13 square units

The area of the figure is 71.13 square units.

Hence Option A is the correct answer.