Question

There is a row of two triangular pyramids and one pentagonal pyramid in a display at a museum. How many lateral faces are there altogethe

Answer 1

Calculate the surface area of a right rectangular prism with dimensions w=12 in.
, l=18 in.
, and h=8 in.
. How many square inches is the surface area

Answer 2

To find the total number of lateral faces, we first need to determine the number of lateral faces for each type of pyramid.

1. **Triangular Pyramid**: A triangular pyramid (tetrahedron) has:
- 4 triangular faces in total.
- 1 base (the triangular base), which means it has \(4 - 1 = 3\) lateral faces.

2. **Pentagonal Pyramid**: A pentagonal pyramid has:
- 6 faces in total (1 pentagonal base and 5 triangular lateral faces).
- Since there is 1 base, it has \(6 - 1 = 5\) lateral faces.

Now, let's calculate the total number of lateral faces in the display:

- There are 2 triangular pyramids:
- Lateral faces from 2 triangular pyramids: \(2 \times 3 = 6\) lateral faces.

- There is 1 pentagonal pyramid:
- Lateral faces from 1 pentagonal pyramid: \(1 \times 5 = 5\) lateral faces.

Finally, we add the lateral faces from both types of pyramids:

\[
6 \text{ (from triangular pyramids)} + 5 \text{ (from pentagonal pyramid)} = 11
\]

Thus, the total number of lateral faces in the display is \( \boxed{11} \).

Answer 3

To calculate the surface area of a right rectangular prism, you can use the formula:

\[
\text{Surface Area} = 2(lw + lh + wh)
\]

where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.

Given:
- \( l = 18 \) in,
- \( w = 12 \) in,
- \( h = 8 \) in.

Now, substitute these values into the formula:

1. Calculate \( lw \):
\[
lw = 18 \times 12 = 216 \, \text{in}^2
\]

2. Calculate \( lh \):
\[
lh = 18 \times 8 = 144 \, \text{in}^2
\]

3. Calculate \( wh \):
\[
wh = 12 \times 8 = 96 \, \text{in}^2
\]

Now sum these areas:
\[
lw + lh + wh = 216 + 144 + 96 = 456 \, \text{in}^2
\]

Finally, calculate the surface area:
\[
\text{Surface Area} = 2(456) = 912 \, \text{in}^2
\]

Thus, the surface area of the right rectangular prism is \( \boxed{912} \) square inches.