Question

Please help, been struggling with this for almost a week now.

Answer 1

`A \approx 1140.3\ units^2`

Explanation:

To solve this problem we first need to find the diameter of the circle. We are told the point
`N` is the circle, so we can assume it is the center of the circle. To find the diameter we can use the Pythagorean Theorem:

`a^2 + b^2 = c^2\\40^2 + 9^2 = c^2\\1600 + 81 = c^2\\1681 = c^2\\√(1681) = c\\41 = c`

The diameter is
`41` units, which means the radius is
`(41)/(2)`. From here we can calculate the area of the circle:

`A_c = \pi r^2\\A_c = \pi ((41)/(2))^2\\A_c = \pi 420.25\\A_c \approx 1320.25`

Now we need to subtract the area of the triangle from the area of the circle. Calculate the area of the triangle:

`A_t = (bh)/(2)\\A_t = (40 * 9)/(2)\\A_t = (360)/(2)\\A_t = 180`

Subtract the triangle area from the circle area to get the area of the shaded area:

`A = A_c - A_t\\A = \pi420.25 - 180\\A = 1140.25431\\A \approx 1140.3\ units^2`