Question

what is the area of this figure?
if necessary, round your answer to the nearest hundredth.
square centimeters

Explanation:

Step1: Calculate the area of the rectangle on the left

The formula for the area of a rectangle is \(A = l\times w\). Here, \(l = 7\) cm and \(w = 7\) cm.
\(A_1=7\times7 = 49\) \(cm^2\)

Step2: Calculate the area of the vertical rectangle

The width is \(2\) cm and the height is \(13\) cm.
\(A_2 = 2\times13=26\) \(cm^2\)

Step3: Calculate the area of the semi - circle

The diameter of the semi - circle is \(6 + 2=8\) cm, so the radius \(r=\frac{8}{2}=4\) cm. The formula for the area of a semi - circle is \(A=\frac{1}{2}\pi r^2\).
\(A_3=\frac{1}{2}\times\pi\times4^2=\frac{1}{2}\times\pi\times16 = 8\pi\approx8\times3.1416 = 25.1328\) \(cm^2\)

Step4: Calculate the total area

\(A = A_1+A_2+A_3\)
\(A=49 + 26+25.1328\)
\(A=100.1328\approx100.13\) \(cm^2\)

Answer:

\(100.13\) square centimeters