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

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 \( \boxed{11} \).

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

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.