select the correct answer from each drop - down menu.
a composite figure is shown.
what is the surface area for each part of the figure? what is the total surface area of the figure?
the surface area of the pyramid is ▶ square feet.
the surface area of the square prism is ▶ square feet.
the surface area of the cube is ▶ square feet.
the total surface area is ▶ square feet.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the surface area of the cube
The formula for the surface area of a cube is $SA = 6s^{2}$, where $s = 6$ ft.
$$
\begin{align*}
SA&=6\times6^{2}\
&=6\times36\
& = 216
\end{align*}
$$
## Step2: Calculate the surface area of the square prism
The surface area of a square prism (excluding the top and bottom where it is attached to other shapes). The base - edge $s = 6$ ft and height $h=20$ ft. The lateral surface area of a square prism $LSA=4sh$
$$
\begin{align*}
LSA&=4\times6\times20\
&=480
\end{align*}
$$
## Step3: Calculate the surface area of the square pyramid
The base of the square pyramid has an edge length $s = 6$ ft. The formula for the lateral surface area of a square pyramid is $LSA=\frac{1}{2}Pl$, where $P = 4s$ (perimeter of the base) and $l = 4$ ft (slant height).
$$
\begin{align*}
P&=4\times6=24\
LSA&=\frac{1}{2}\times24\times4\
&=48
\end{align*}
$$
## Step4: Calculate the total surface area
$$
\begin{align*}
\text{Total SA}&=216 + 480+48\
&=744
\end{align*}
$$

# Answer:
The surface area of the cube is $216$ square feet. The surface area of the square prism is $480$ square feet. The surface area of the pyramid is $48$ square feet. The total surface area is $744$ square feet.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Calculate the surface area of the cube

Step2: Calculate the surface area of the square prism

Step3: Calculate the surface area of the square pyramid

Step4: Calculate the total surface area

Answer: