Question

what is the area of this figure?

Explanation:

Step1: Divide the figure into three parts

The figure can be divided into a rectangle with length \(9\) ft and width \(2\) ft, a trapezoid with parallel sides \(5\) ft and \(4 + 2=6\) ft and height \(9 - 7=2\) ft, and a square with side \(4\) ft.

Step2: Calculate the area of each part

• Area of the rectangle:

The formula for the area of a rectangle is \(A = l\times w\). For the rectangle with \(l = 9\) ft and \(w = 2\) ft, \(A_1=9\times2 = 18\) square - feet.

• Area of the trapezoid:

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a = 5\) ft, \(b=6\) ft, and \(h = 2\) ft. Then \(A_2=\frac{(5 + 6)\times2}{2}=11\) square - feet.

• Area of the square:

The formula for the area of a square is \(A = s\times s\). For the square with \(s = 4\) ft, \(A_3=4\times4=16\) square - feet.

Step3: Sum up the areas of all parts

\(A=A_1 + A_2+A_3\). Substitute \(A_1 = 18\), \(A_2 = 11\), and \(A_3 = 16\) into the formula. \(A=18 + 11+16=45\) square - feet.

Answer:

The area of the figure is \(45\) square - feet.