Question

The curved part of this figures is a semicircle.

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


14+16.25π units²

28+16.25π units²

14+8.125π units²

28+8.125π units²
Coordinate plane with axes labeled x and y. A closed figure is formed by two segments and a semicircle. A segment extends from negative 4 comma negative 2 to negative 4 comma 2. Another segment extends from negative 4 comma 2 to 3 comma 2. A semicircle extends from 3 comma 2 to negative 4 comma negative 2.

Answer 1

The area of a shape is the amount of space on the shape.

The best approximation for the area of the figure is $14 + 16.25\pi$

How to determine the area of the figure

Start by calculating the diameter of the semicircle using the following distance formula:

$d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2}$

So, we have:

$d = \sqrt{(-4 -3)^2 +(-2 -2)^2}$

$d = \sqrt{65}$

Divide by 2, to calculate the radius

$r = \frac{\sqrt{65}}{2}$

So, the area of the semicircle is:

$A = \frac{\pi r^2}{2}$

This gives

$A = \pi (\frac{\sqrt{65}}{2})^2$

$A = \frac{65}{4}\pi$

$A = 16.25\pi$

Next, we calculate the area of the triangle using:

$A = 0.5 * B * H$

Where:

$B = 3 -(-4)$

$B = 7$

$H= 2 - (-2)$

$H = 4$

So, we have:

$A = 0.5 * 7 * 4$

$A = 14$

The area of the figure is then calculated as:

$A = 14 + 16.25\pi$

Hence, the best approximation for the area of the figure is $14 + 16.25\pi$

Read more about areas at:

https://brainly.com/question/10090807