Question

the sector of a circle shown has center at o. the radius of the circle has length 5. the arc xzy has length 7. to the nearest tenth, what is the shaded area of the sector?

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector is \(A=\frac{1}{2}r\times l\), where \(r\) is the radius of the circle and \(l\) is the arc - length of the sector.

Step2: Substitute the given values into the formula

Given that \(r = 5\) and \(l=7\).
Substitute these values into the formula \(A=\frac{1}{2}\times5\times7\).
First, calculate \(\frac{1}{2}\times5=\frac{5}{2}\), then \(\frac{5}{2}\times7=\frac{35}{2}=17.5\)

Answer:

\(17.5\)