Your answer would be 390.04
To find the area of the shaded portion, we need to find both the area of the circle and the area of the triangle, so that we can subtract the triangle from the circle.
The equation for the area of a circle is πr², so in this case we get π × 12² = 144π.
To find the area of the triangle, we must notice that because of the double markings on each side length, it is an equilateral triangle. This means that each angle inside is 60°. We can use this fact to find the length of a side of the triangle, which we can then use to find the area.
You can split up the triangle in the way I've drawn in the image to form a right-angled triangle, and this allows you to use trigonometry to find the side length. In this case, the length 12 is the hypotenuse, and the length we're looking for is adjacent to the 60° angle, so we must use cosine.
Then we do cos(60) × 12 = 1/2 × 12 = 6. We need to double this length.
Now that we have the length of a side of the triangle, we can find the area by doing area = 1/2 × A × B × sinC where A and B are lengths and C is the angle between them. This means we'll get 1/2 × 12 × 12 × sin(60) = 72 × [tex]\frac{\sqrt{3} }{2}[/tex] = 36√3.
Finally, we take the area of the circle that we found earlier and subtract 9√3 from it, giving us 144π - 36√3 = 452.4 - 62.4 = 390.04
I hope this helps! Let me know if you have any questions :)
