Question

The shape is a Rectangular Prism. Find the TOTAL surface area of the shape.
2cm, 5cm, 4cm.

Then find the LATERAL surface area of the shape.

Answer 1

To find the total surface area and the lateral surface area of a rectangular prism, we can use the following formulas:

1. **Total Surface Area (TSA)** of a rectangular prism is given by:
\[
\text{TSA} = 2lw + 2lh + 2wh
\]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.

2. **Lateral Surface Area (LSA)** of a rectangular prism is given by:
\[
\text{LSA} = 2lh + 2wh
\]
which excludes the top and bottom surfaces.

Given dimensions:
- Length \( l = 5 \, \text{cm} \)
- Width \( w = 4 \, \text{cm} \)
- Height \( h = 2 \, \text{cm} \)

### Calculating the Total Surface Area:
Using the TSA formula:
\[
\text{TSA} = 2lw + 2lh + 2wh
\]
Substituting the values:
- \( lw = 5 \, \text{cm} \times 4 \, \text{cm} = 20 \, \text{cm}^2 \)
- \( lh = 5 \, \text{cm} \times 2 \, \text{cm} = 10 \, \text{cm}^2 \)
- \( wh = 4 \, \text{cm} \times 2 \, \text{cm} = 8 \, \text{cm}^2 \)

Now plug these into the TSA formula:
\[
\text{TSA} = 2(20) + 2(10) + 2(8) = 40 + 20 + 16 = 76 \, \text{cm}^2
\]

### Calculating the Lateral Surface Area:
Using the LSA formula:
\[
\text{LSA} = 2lh + 2wh
\]
Substituting the values:
\[
\text{LSA} = 2(10) + 2(8) = 20 + 16 = 36 \, \text{cm}^2
\]

### Summary:
- **Total Surface Area**: \( 76 \, \text{cm}^2 \)
- **Lateral Surface Area**: \( 36 \, \text{cm}^2 \)