Question

The shape is a Rectangular Prism. height is 2cm, width is 5cm, length is 4cm
Find the TOTAL surface area of the shape.
40 cm 2
20 cm 2
22 cm 2
76 cm 2

Answer 1

To find the total surface area (TSA) of a rectangular prism, you can use the formula:

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

where:
- \( l \) = length
- \( w \) = width
- \( h \) = height

For the values given:
- height (\( h \)) = 2 cm
- width (\( w \)) = 5 cm
- length (\( l \)) = 4 cm

Plugging the values into the formula:

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

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

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

4. Now sum these areas:
\[
lw + lh + wh = 20 + 8 + 10 = 38 \, \text{cm}^2
\]

5. Finally, multiply by 2 to find the total surface area:
\[
\text{TSA} = 2 \times 38 = 76 \, \text{cm}^2
\]

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