Question

PLEASE MATH HELP

The curved part of this figure is a semicircle.

What is the best approximation for the area of this figure?


10.5+14.5π units²

21+7.25π units²

10.5+7.25π units²

21+14.5π units²

Answer 1

The best answer would be the third option or C.

Answer 2

ANSWER


`10.5 + 7.25\pi \: {units}^(2)`

Step-by-step explanation

The figure is made up of a triangle and a semicircle.

The area of the triangle is


`= (1)/(2) * base * height`


`= (1)/(2) * 7 * 3`


`= (21)/(2)`


`= 10.5 \: units \: square`

The area of the semicircular part is


`= \frac{\pi \: {d}^(2) }{8}`

We can find the diameter squared using the Pythagoras Theorem.


`{d}^(2) = {7}^(2) + {3}^(2)`


`{d}^(2) = 49+ 9`


`{d}^(2) = 58`

We substitute this into the formula for finding the area of the semicircle to get;


`= (58\pi)/(8)`


`= 7.25\pi \: {units}^(2)`

Therefore the area of the figure is


`10.5 + 7.25\pi \: {units}^(2)`

See diagram in attachment.