Question

in circle g with m∠fgh = 34° and fg = 13, find the area of sector fgh. round to the nearest hundredth. answer attempt 1 out of 3 units² submit answer

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle with radius \( r \) and central angle \( \theta \) (in degrees) is \( A=\frac{\theta}{360}\times\pi r^{2} \). Here, the radius \( r = FG=13 \) and the central angle \( \theta = m\angle FGH = 34^{\circ} \).

Step2: Substitute the values into the formula

Substitute \( \theta = 34^{\circ} \) and \( r = 13 \) into the formula:
\( A=\frac{34}{360}\times\pi\times(13)^{2} \)

First, calculate \( (13)^{2}=169 \). Then, \( \frac{34}{360}\times\pi\times169=\frac{34\times169\times\pi}{360} \).

Calculate \( 34\times169 = 5746 \). So, \( A=\frac{5746\pi}{360} \).

Simplify \( \frac{5746}{360}\approx15.9611 \). Then, \( A\approx15.9611\times\pi \).

Using \( \pi\approx3.1416 \), we get \( A\approx15.9611\times3.1416\approx50.13 \).

Answer:

\( 50.13 \)