Question

area of irregular shapes
score: 0/5 penalty: 0.25 off
question
find the area of the figure below, composed of a rectangle and one semicircle, with another semicircle removed. round to the nearest tenths place.
11
4
answer attempt 1 out of 2
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Explanation:

Step1: Analyze the area composition

The area of the figure is the area of the rectangle. The area formula of a rectangle is \(A = length\times width\).

Step2: Determine the values of length and width

The length of the rectangle is \(l = 11\), and the width \(w=4\) (since the diameter of the semicircles is 4, and the width of the rectangle is equal to the diameter of the semicircles).

Step3: Calculate the area of the rectangle

Using the formula \(A = l\times w\), we substitute \(l = 11\) and \(w = 4\) into it. So \(A=11\times4=44\).
The two - semicircles (one added and one removed) have the same area (because they have the same diameter \(d = 4\), so radius \(r=\frac{d}{2}=2\), and the area of a semicircle is \(A_{semicircle}=\frac{1}{2}\pi r^{2}\)). Their combined effect on the total area is zero. Rounding 44 to the nearest tenths place gives 44.0.

Answer:

44.0