Exercise 28 Page 851

We are asked to find the area of the monolith that lies above the ground. Therefore, for the lateral area of the prism $L$ we should add only one area of the base, $B.$ Since the base is a rectangle that is $4$ feet by $1$ foot, its area is $B=4\cdot 1=4$ square feet. The lateral area is equal to $L=Ph,$ where $P$ is the perimeter of the base and $h$ is the height of the prism. This tells us that $P=2\cdot 4+2\cdot 1=10$ feet. Therefore, $L=Ph=10\cdot 9=90$ square feet. Therefore, the monolith's total surface area above the ground $S_{\text{total}}$ is the sum of one base area and the lateral area. Finally, we find that the area in square feet of the structure's surfaces that lies above the ground is $94$ square feet.