Question

directions - use the diagram to find the measure of the sector area:
*use 3.14 in place of π

area of sector = (round to two decimal places)

Explanation:

Step1: Recall sector area formula

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

Step2: Identify values

Here, \( \theta = 100^{\circ} \), \( r = 7\space\text{cm} \), and \( \pi = 3.14 \).

Step3: Substitute values into formula

First, calculate \( r^{2} \): \( 7^{2}=49 \). Then, calculate \( \pi r^{2} \): \( 3.14\times49 = 153.86 \). Next, find the fraction of the circle the sector represents: \( \frac{100^{\circ}}{360^{\circ}}=\frac{5}{18} \). Finally, multiply this fraction by \( \pi r^{2} \): \( A=\frac{5}{18}\times153.86 \).

Step4: Perform the multiplication

\( \frac{5}{18}\times153.86=\frac{769.3}{18}\approx42.74 \) (rounded to two decimal places).

Answer:

\( 42.74\space\text{cm}^2 \)