Question

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

Explanation:

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

We can divide the figure into 3 rectangles and 1 semi - circle.

Step2: Calculate the area of the first rectangle

The first rectangle has dimensions 3 ft by 10 ft. The area formula for a rectangle is $A = l\times w$. So, $A_1=3\times10 = 30$ square feet.

Step3: Calculate the area of the second rectangle

The second rectangle has length $24$ ft and width $4$ ft. So, $A_2 = 24\times4=96$ square feet.

Step4: Calculate the area of the third rectangle

The third rectangle has dimensions 14 ft by 5 ft. So, $A_3=14\times5 = 70$ square feet.

Step5: Calculate the area of the semi - circle

The diameter of the semi - circle is 4 ft, so the radius $r = 2$ ft. The area formula for a semi - circle is $A=\frac{1}{2}\pi r^{2}$. So, $A_4=\frac{1}{2}\pi\times(2)^{2}=2\pi\approx 2\times3.14 = 6.28$ square feet.

Step6: Calculate the total area

The total area $A = A_1+A_2+A_3+A_4$. So, $A=30 + 96+70+6.28=202.28$ square feet.

Answer:

$202.28$ square feet