Question

This figure is made up of a quadrilateral and a semicircle.

What is the area of this figure?

Use 3.14 for pi. Round your answer to the nearest tenth.

A.) 22.8 units²

B.) 40.4 units²

C.) 45.5 units²

D.) 74.5 units²

Answer 1

The correct option is B. The area of the figure is 40.4 units².

Explanation:

The line AB divides the figure in two parts one is a rectangle and another is semicircle.

The distance formula is

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

The length of AB is

`AB=√((2+3)^2+(4-2)^2)=√(25+4)=√(29)`

The length of AD is

`AD=√((-1+3)^2+(-3-2)^2)=√(4+25)=√(29)`

Since AB=AD, therefore ABCD is a square. The area of the of square is

`A_1=a* a=√(29)* √(29) =29`

The area of square is 29 units².

The area of a semicircle is

`A_2=(\pi)/(2)r^2`

Since AB is the diameter of the semicircle, therefore the radius of the semicircle is

`r=(d)/(2)=(√(29))/(2)`

The area of the semicircle is

`A_2=(3.14)/(2)((√(29))/(2))^2=40.3825`

The area of the figure is

`A=A_1+A_2=29+11.2825=40.3825\approx 40.4`

Therefore the area of the figure is 40.4 units². Option B is correct.