Question

8 formula 0.5 points given the following composite figure, d = 6.6 cm and w = 11.0 cm. what is the area of the figure? use 3.14 for pi, and round your answer to the nearest hundredth. do not include \cm²\ with your response. answer

Explanation:

Step1: Identify the composite figure components

The composite figure consists of a rectangle and two semicircles (which form a full circle). The diameter of the circle is \( d = 6.6 \) cm, so the radius \( r=\frac{d}{2}=\frac{6.6}{2} = 3.3 \) cm. The length of the rectangle is \( w = 11.0 \) cm and the width is \( d = 6.6 \) cm.

Step2: Calculate the area of the rectangle

The area of a rectangle is given by \( A_{rectangle}=length\times width \). Substituting the values, we get \( A_{rectangle}=11.0\times6.6 = 72.6 \)

Step3: Calculate the area of the circle

The area of a circle is given by \( A_{circle}=\pi r^{2} \). Using \( \pi = 3.14 \) and \( r = 3.3 \), we have \( A_{circle}=3.14\times(3.3)^{2} \). First, calculate \( (3.3)^{2}=10.89 \), then \( A_{circle}=3.14\times10.89 = 34.1946 \)

Step4: Calculate the total area of the composite figure

The total area \( A = A_{rectangle}+A_{circle} \). Substituting the values, we get \( A=72.6 + 34.1946=106.7946 \)

Step5: Round to the nearest hundredth

Rounding \( 106.7946 \) to the nearest hundredth gives \( 106.79 \)

Answer:

106.79