Question

The image below is a triangle drawn inside a circle with center O: A triangle is shown inscribed inside a circle. The leg of the triangle labeled 8 inches passes through the center of the circle, O. The other two legs are labeled as 4 inches and 5 inches. Which of the following expressions shows the area, in square inches, of the circle? (π = 3.14) 3.14 ⋅ 42 3.14 ⋅ 52 3.14 ⋅ 5 3.14 ⋅ 22

Answer 1

A.
`3.14*4^2`

Explanation:

We have been given that a triangle is inscribed inside a circle. The leg of the triangle labeled 8 inches passes through the center of the circle, O. The other two legs are labeled as 4 inches and 5 inches.

The leg with 8 inches length passes through the center, so it will be the diameter of the circle.

To find the area of the circle, we will divide diameter by 2 to find radius of circle.

`r=(8)/(2)`

`r=4`

`\text{Area of circle}=\pi r^2`

`\text{Area of circle}=3.14*4^2`

Upon looking at our given choices, we can see that option A is the correct choice.

Answer 2

The area of a circle is given in terms of its radius by
A = π · r²

Your circle has r=4 (half the diameter) and you want π=3.14. Using these values in the formula gives
A = 3.14 · 4²

This matches your first selection
3.14 · 4²