Question

find the area of the figure below, composed of a rectangle with a semicircle removed from it. round to the nearest tenths place. 11 6 answer attempt 1 out of 2 submit answer

Explanation:

Step1: Calculate the area of the rectangle

The area formula for a rectangle is \(A_{\text{rectangle}}=\text{length}\times\text{width}\). Here, length \(l = 11\) and width \(w=6\). So, \(A_{\text{rectangle}}=11\times6 = 66\).

Step2: Calculate the area of the semi - circle

The diameter of the semi - circle is equal to the width of the rectangle, so \(d = 6\), and the radius \(r=\frac{d}{2}=\frac{6}{2}=3\). The area formula for a semi - circle is \(A_{\text{semicircle}}=\frac{1}{2}\pi r^{2}\). Substituting \(r = 3\) into the formula, we get \(A_{\text{semicircle}}=\frac{1}{2}\times\pi\times3^{2}=\frac{9\pi}{2}\approx\frac{9\times3.14}{2}=14.13\).

Step3: Calculate the area of the composite figure

The area of the figure \(A=A_{\text{rectangle}}-A_{\text{semicircle}}\). Substitute the values of \(A_{\text{rectangle}}\) and \(A_{\text{semicircle}}\): \(A = 66-14.13=51.87\approx51.9\).

Answer:

\(51.9\)