Question

PLEASE HELP! Urgent!!!

Which of the following expressions represents the area of the composite figure ( i said 18 pi + 35 and it said it was wrong)

Answer 1

`(9)/(2)\pi +35`

Explanation:

The area of trapezoid is given by the formula:

`A=(1)/(2)(b_1+b_2)h`

Where

A is the area

b_1 is base 1

b_2 is base 2, and

h is the height

Looking at the figure, base 1 is the left line which goes from y = 3 to y = 3, so 6 units. Also, base 2 is the right line which goes from y = -3 to y =5, so 8 units.

The height is the horizontal distance in the middle, which goes from x = -2 to x = 3, so 5 units. Hence area of trapezoid is:

`A=(1)/(2)(b_1+b_2)h\\A=(1)/(2)(6+8)*5\\A=35`

Now, area of semicircle is:

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

Where

A is the area

r is the radius

Looking at the figure, the diameter (twice radius) goes from y = -3 to y = 3, so 6 units. But radius is half of that, so 3 units. Hence area of semicircle is:

`A=(\pi r^2)/(2)\\A=(\pi (3)^2)/(2)\\A=(9)/(2) \pi`

Total area of the figure is
`(9)/(2)\pi +35`