Question

what is the area of this figure?

Explanation:

Step1: Divide the figure into rectangles and a triangle

We can divide the figure into three rectangles and one right - triangle.

Step2: Calculate the area of the first rectangle

The first rectangle has dimensions 3 ft by 4 ft. The area formula for a rectangle is $A = l\times w$. So, $A_1=3\times4 = 12$ square feet.

Step3: Calculate the area of the second rectangle

The second rectangle has dimensions $(3 + 5+2)$ ft by 4 ft. So, $A_2=(3 + 5+2)\times4=10\times4 = 40$ square feet.

Step4: Calculate the area of the third rectangle

The third rectangle has dimensions 2 ft by 8 ft. So, $A_3=2\times8 = 16$ square feet.

Step5: Calculate the area of the triangle

The base of the triangle is $(3 + 5+2+2)$ ft and the height is $(12 - 4)$ ft. The area formula for a triangle is $A=\frac{1}{2}\times b\times h$. Here, $b = 12$ ft and $h = 8$ ft. So, $A_4=\frac{1}{2}\times12\times8=48$ square feet.

Step6: Calculate the total area

The total area $A = A_1+A_2+A_3+A_4$. So, $A=12 + 40+16+48=116$ square feet.

Answer:

116 square feet