Question

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

Answer 1

Answer:

$A \approx 1140.3\ units^2$

Step-by-step 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:

$a^2 + b^2 = c^2\\40^2 + 9^2 = c^2\\1600 + 81 = c^2\\1681 = c^2\\\sqrt{1681} = c\\41 = c$

The diameter is $41$ units, which means the radius is $\frac{41}{2}$. From here we can calculate the area of the circle:

$A_c = \pi r^2\\A_c = \pi (\frac{41}{2})^2\\A_c = \pi 420.25\\A_c \approx 1320.25$

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

$A_t = \frac{bh}{2}\\A_t = \frac{40 \times 9}{2}\\A_t = \frac{360}{2}\\A_t = 180$

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

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