Question

Start by finding the area of the base of the prism. Solve on paper, and then enter your answer on Zearn. You can use the Zearn calculator to help with your calculations.
3D shape with L-shaped base labeled with side lengths in cm: 10, 2, 6, 4. A side length of 3 cm connects the two bases.
Area of the base, B Height of the prism, h Volume, V = B · h
cm
2
? cm ? cm
3

Answer 1

To find the area of the base of the prism with an L-shaped base, we'll first divide the L-shape into two rectangles.

The L-shape can be visualized as consisting of:
- Rectangle 1 with dimensions 10 cm (length) and 6 cm (width).
- Rectangle 2 with dimensions 4 cm (length) and 2 cm (width).

**Step 1: Calculate the area of Rectangle 1.**
Area of Rectangle 1 = length × width
\[
\text{Area of Rectangle 1} = 10 \, \text{cm} \times 6 \, \text{cm} = 60 \, \text{cm}^2
\]

**Step 2: Calculate the area of Rectangle 2.**
Area of Rectangle 2 = length × width
\[
\text{Area of Rectangle 2} = 4 \, \text{cm} \times 2 \, \text{cm} = 8 \, \text{cm}^2
\]

**Step 3: Calculate the total area of the L-shaped base.**
Total area of the base, \( B \)
\[
B = \text{Area of Rectangle 1} + \text{Area of Rectangle 2} = 60 \, \text{cm}^2 + 8 \, \text{cm}^2 = 68 \, \text{cm}^2
\]

**Step 4: Identify the height of the prism.**
The height of the prism, \( h \), is given as 3 cm.

Now you have:
- Area of the base \( B = 68 \, \text{cm}^2 \)
- Height of the prism \( h = 3 \, \text{cm} \)

**Step 5: Calculate the volume \( V \) of the prism.**
The formula for volume is:
\[
V = B \cdot h
\]
\[
V = 68 \, \text{cm}^2 \times 3 \, \text{cm} = 204 \, \text{cm}^3
\]

**Final Answers:**
- Area of the base, \( B = 68 \, \text{cm}^2 \)
- Height of the prism, \( h = 3 \, \text{cm} \)
- Volume of the prism, \( V = 204 \, \text{cm}^3 \)

Make sure to enter the area of the base as \( 68 \, \text{cm}^2 \) on Zearn.