Question

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

Explanation:

Step1: Calculate the area of the rectangle on the top

The formula for the area of a rectangle is \(A = l\times w\). The length \(l = 11\) m and the width \(w=2\) m.
\(A_1=11\times2 = 22\) square meters.

Step2: Calculate the area of the middle - part rectangle

The length \(l = 5\) m and the width \(w=(11 - 9)=2\) m.
\(A_2 = 5\times2=10\) square meters.

Step3: Calculate the area of the bottom - part rectangle

The length \(l=(3 + 2)=5\) m and the width \(w = 2\) m.
\(A_3=5\times2 = 10\) square meters.

Step4: Calculate the area of the \(\frac{3}{4}\) - circle

The radius \(r=(3 + 2)=5\) m. The formula for the area of a circle is \(A=\pi r^{2}\). For a \(\frac{3}{4}\) - circle, \(A_4=\frac{3}{4}\pi r^{2}\).
Substitute \(r = 5\) into the formula: \(A_4=\frac{3}{4}\times\pi\times5^{2}=\frac{3}{4}\times\pi\times25=\frac{75\pi}{4}\approx58.90\) square meters.

Step5: Sum up the areas

\(A=A_1 + A_2+A_3+A_4\)
\(A=22 + 10+10 + 58.90\)
\(A=100.90\) square meters.

Answer:

\(100.90\)