Question

1. 6) 9.6 ft 13.8 ft 9.4 ft 10.2 ft 3.4 yd 9.7 yd 12 yd surface area = surface area =

Explanation:

Step1: Calculate the surface area of the parallelogram - triangle composite (Problem 5)

The figure in problem 5 is composed of a parallelogram and a right - triangle.
The area of the parallelogram \(A_{p}=b\times h\), where \(b = 9.6\) ft and \(h=9.4\) ft. So \(A_{p}=9.6\times9.4 = 90.24\) \(ft^{2}\).
The area of the right - triangle \(A_{t}=\frac{1}{2}\times base\times height\), with base \(b = 10.2\) ft and height \(h = 9.4\) ft. So \(A_{t}=\frac{1}{2}\times10.2\times9.4=47.94\) \(ft^{2}\).
The total surface area \(A = A_{p}+A_{t}\).

Step2: Calculate the surface area of the rectangular prism (Problem 6)

The formula for the surface area of a rectangular prism \(SA=2(lw + lh+wh)\), where \(l = 12\) yd, \(w = 3.4\) yd, and \(h = 9.7\) yd.
First, calculate \(lw=12\times3.4 = 40.8\) \(yd^{2}\), \(lh=12\times9.7=116.4\) \(yd^{2}\), \(wh=3.4\times9.7 = 32.98\) \(yd^{2}\).
Then \(lw+lh + wh=40.8+116.4 + 32.98=190.18\) \(yd^{2}\).
Multiply by 2: \(SA = 2\times190.18=380.36\) \(yd^{2}\).

Answer:

1. \(90.24 + 47.94=138.18\) \(ft^{2}\)
2. \(380.36\) \(yd^{2}\)