Question

b) area:____ perimeter:____

Explanation:

Step1: Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the parallel sides and \(h\) is the height.
The upper base \(a=4 + 2+3+2 + 4=15\) feet, the lower base \(b = 17\) feet, and the height \(h = 4\) feet.
So the area of the trapezoid is \(A_{trapezoid}=\frac{(15 + 17)\times4}{2}=\frac{32\times4}{2}=64\) square feet.

Step2: Calculate the area of the rectangle to be subtracted

The area of a rectangle is \(A = l\times w\), where \(l\) is the length and \(w\) is the width.
Here \(l = 3\) feet and \(w=2\) feet, so \(A_{rectangle}=3\times2 = 6\) square feet.

Step3: Calculate the final area

The area of the shape is \(A=A_{trapezoid}-A_{rectangle}\)
\(A=64 - 6=58\) square feet.

Step4: Calculate the perimeter

The perimeter is the sum of all the outer - side lengths.
\(P=5 + 17+5+(4 + 2+3+2 + 4)=5 + 17+5+15=42\) feet.

Answer:

Area: \(58\) square feet, Perimeter: \(42\) feet