Question

I have the 2nd and last one not sure of the 1st or 3rd

Answer 1

Given:

• Length of base(cube) = 6 ft

,

• Height of square prism = 20 ft

,

• Height of pyramid =4 ft

Since it is a composite figure, the surface of some sides will not be included in the surface area.

Let's solve for the following:

• (a). The surface area of the pyramid.

To find the surface area of the pyramid, apply the formula:

$SA=A+\frac{1}{2}ps$

Where:

A is the area of the base

p is the perimeter of the base

s is the slant height.

To find the slant height, apply Pythagorean theorem:

$\begin{gathered} s=\sqrt{(4)^2+(\frac{6}{2})^2} \\ \\ s=\sqrt{16+9}=\sqrt{25}=5\text{ ft} \end{gathered}$

We have:

$\begin{gathered} SA=(6*6)+\frac{1}{2}(6*4)*5 \\ \\ SA=36+\frac{1}{2}(24)*5 \\ \\ SA=36+60 \\ \\ SA=96\text{ ft}^2 \end{gathered}$

The surface area of the pyramid is 96 ft².

• (b). Surface area of the square prism.

Apply the formula:

$\begin{gathered} SA=3ah \\ \\ SA=4(6)(20) \\ \\ SA=480\text{ ft}^2 \end{gathered}$

The surface area of the square prism is 480 ft².

• (c). Surface area of the cube.

To find the surface area of the cube, we have:

$\begin{gathered} SA=6a^2 \\ \\ SA=6(6)^2 \\ \\ SA=216\text{ ft}^2 \end{gathered}$

The surface area of the cube is 216 ft²

The total surface area will be:

T = Surface area of pyramid + surface area of prism + surface area of cube - area of base

T = 96 + 480 + 216 - 36

T = 756 ft²

ANSWER:

Surface area of the pyramid is 96 ft².

Surface area of the square prism is 480 ft².

Surface area of the cube is 216 ft²

Total surface area is 756 ft²