Exercise 7 Page 656

A sector of a circle is the region bounded by an arc of the circle and the two radii to the arc's endpoints.

The area of a sector of a circle is the product of the area of the circle and the measure of the arc divided by 360. Area of sectorAOB: m AB/360* π r^2Consider the given circle.

In the diagram, we are given that the area of sector RSQ is 27.93 square feet. The central angle m∠ RSQ is 50^(∘). We first need to calculate the measure of the minor arc, mRQ. Recalling that the measure of an arc equals its corresponding central angle, we can identify mRQ as follows. m∠RSQ=50^(∘) ⇔ mRQ= 50^(∘) We can now find the measure of the major arc mRTQ by subtracting mRQ to 360^(∘). mRTQ=360^(∘)- 50^(∘) ⇔ mRTQ= 310^(∘)
To find the area of the sector RTQ we also need the value of r or r^2. To do so, let's substitute A= 27.93 and mRQ= 50 in the formula of the area of a sector and solve of r^2

We found that r^2≈ 64.011 and mRTQ= 310. Let's substitute them in the formula to find the area of sector RTQ.

Thus, the area of sector RTQ is about 173.166 square feet.