Question

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

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Answer 1

`2,642.08cm^2`

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`)