Answer: 5.1 cm² is the correct answer.
Step-by-step explanation:
to find the area of the shaded region. We want to find the volume of the sector and minus the. Now if you excuse me, the area of the sector minus the area of the triangle. Okay, so let's start with the sector. The area of the sector would be 80° out of 360 times the area of a circle, which is pi times the radius which is five squared. And it will subtract the area of the triangle. All right. Since it's an isosceles triangle, we could turn this into two right triangles. And This would be a 40° angle. And we can find X. Which would be the base of the triangle. Using silk Ayatollah using trig. We would want to find the opposite of 40° and we have the hypotenuse, So opposite and hypotenuse is signed. So we can say the sign of 40° is equal to opposite over hypotenuse and five times the sine of 40 equals double that. And we've got the full base of the triangle. So The area of the triangle would be 1/2 A base. If we double it would be 10 signed 40. And then times the height which we again could use um I'll call it why? We could use Kassian. We could say the Kassian of 40° equals Y over five. So 5 cosine, 40 is equal to the height of the triangle. Okay, so putting this all together, I'm gonna do it all at once. Right into Desormeaux's As we see it here, 80 out of 360 tons. Spy five squared. And then we're going to subtract The area of the triangle, which is 1/2 times 10. Sign 40. Make sure you're in degree mode, right? And then we multiply that by five co sign 40 mm. Hmm. And we'll round to the nearest 10th to get 5.1.
