Question

Find the area of the following circle if segment HF measures 58cm.​

Answer 1

Answer:

$2,642.08cm^2$

Step-by-step explanation:

to find the area of the circle we need the following formula:

$a=\pi r^2$

where $\pi$ is a constant ($\pi=3.1416$) and $r$ is the radius of the circle.

The radius is the measure of the line from the center of the circle to a point on the circumference.

The HF measurement is a line that crosses the circle in the middle passing through the center, this is known as the diameter of the circle:

$d=58cm$

and from the symmetry of the circle, it is known that if we divide the diameter in half we obtain the radius:

$r=d/2\\\\r=58cm/2\\\\r=29cm$

and now we can use the formula for the area:

$a=\pi r^2$

substituting the radius:

$a=\pi (29cm)^2\\a=\pi(841cm^2)\\a=2,642.08cm^2$

which is the second option.

(Note: option 4 is wrong because it has $cm$ units instead of $cm^2$)