a The area of the structure's surfaces that lie above the ground consists of 5 rectangles.
B
b Use the fact that 1 yard is 3 feet, so 1 square yard is 3^2=9 square feet.
A
a 94 square feet
B
b About 10.44 square yards
Practice makes perfect
a A monolith that is 9 feet by 4 feet by 1 foot that lies on the ground can be modeled by the following rectangular prism.
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* 1=4 square feet.
Base Area: B=4 ft^2
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* 4+2* 1=10 feet. Therefore, L=Ph=10* 9=90 square feet.
Lateral Area: L=90 ft^2
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.
b We are asked to find the answer from Part A in square yards. Since 1 yard is 3 feet, 1 square yard is 3^2=9 square feet. From Part A we know the following.
\begin{gathered}
S_\text{total}=94\,\text{ft}^2
\end{gathered}
Since 9 ft^2=1 yd^2, we get that 1= 1 yd^29 ft^2. This tells us that we should multiply the answer from Part A by 1 yd^29 ft^2. Let's do it!
\begin{aligned}
S_\text{total}&=94\,\cancel{\text{ft}^2}\ \cdot\ \frac{1\,\text{yd}^2}{9\,\cancel{\text{ft}^2}}\\ &=\dfrac{94}{9}\,\text{yd}^2\approx 10.44\,\text{yd}^2
\end{aligned}
Therefore, the area in square yards is equal to about 10.44.
