Question

3 cm
5 cm
9 cm
4 cm
8 cm
7 cm
if necessary, round your answer to the nearest hundredth.
square centimeters
submit

Explanation:

Step1: Divide the shape into rectangles and a semi - circle

We can divide the given shape into two rectangles and a semi - circle. The first rectangle has dimensions 3 cm by 5 cm, the second rectangle has dimensions (7 + 4) cm by 8 cm, and the semi - circle has a diameter equal to 3 cm.

Step2: Calculate the area of the first rectangle

The area formula for a rectangle is $A = l\times w$. For the first rectangle with $l = 5$ cm and $w = 3$ cm, $A_1=5\times3 = 15$ $cm^2$.

Step3: Calculate the area of the second rectangle

The length of the second rectangle is $7 + 4=11$ cm and width is 8 cm. Using the rectangle area formula $A = l\times w$, $A_2 = 11\times8=88$ $cm^2$.

Step4: Calculate the area of the semi - circle

The formula for the area of a circle is $A=\pi r^2$, and for a semi - circle it is $A=\frac{1}{2}\pi r^2$. The diameter of the semi - circle is 3 cm, so the radius $r=\frac{3}{2}$ cm. Then $A_3=\frac{1}{2}\pi(\frac{3}{2})^2=\frac{1}{2}\pi\times\frac{9}{4}=\frac{9\pi}{8}\approx\frac{9\times3.14}{8}=3.5325$ $cm^2$.

Step5: Calculate the total area of the shape

The total area $A = A_1+A_2+A_3$. Substitute the values: $A=15 + 88+3.5325=106.5325\approx106.53$ $cm^2$.

Answer:

$106.53$