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

$10.5 + 7.25\pi \: {units}^{2}$

EXPLANATION

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

The area of the triangle is

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

$= \frac{1}{2} \times 7 \times 3$

$= \frac{21}{2}$

$= 10.5 \: units \: square$

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;

$= \frac{58\pi}{8}$

$= 7.25\pi \: {units}^{2}$

Therefore the area of the figure is

$10.5 + 7.25\pi \: {units}^{2}$

See diagram in attachment.