Question

the width 5 cm
The height 2 cm
The length 4 cm

The shape is a Rectangular Prism.

Find the TOTAL surface area of the shape.

40 cm 2

20 cm 2

22 cm 2

76 cm 2

Answer 1

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

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

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

Given:
- Length \( l = 4 \) cm
- Width \( w = 5 \) cm
- Height \( h = 2 \) cm

Now, substitute the values into the formula:

1. Calculate \( lw \):
\[
lw = 4 \, \text{cm} \times 5 \, \text{cm} = 20 \, \text{cm}^2
\]

2. Calculate \( lh \):
\[
lh = 4 \, \text{cm} \times 2 \, \text{cm} = 8 \, \text{cm}^2
\]

3. Calculate \( wh \):
\[
wh = 5 \, \text{cm} \times 2 \, \text{cm} = 10 \, \text{cm}^2
\]

Now, sum these areas:

\[
lw + lh + wh = 20 \, \text{cm}^2 + 8 \, \text{cm}^2 + 10 \, \text{cm}^2 = 38 \, \text{cm}^2
\]

Finally, multiply by 2 to get the total surface area:

\[
\text{Total Surface Area} = 2 \times 38 \, \text{cm}^2 = 76 \, \text{cm}^2
\]

Therefore, the total surface area of the rectangular prism is \( \boxed{76 \, \text{cm}^2} \).