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.

Question

3D shape with L-shaped base labeled with side lengths in cm: 20, 5, 5, 15. A side length of 5 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, we need to calculate the area of the L-shaped base given the side lengths.

The L-shaped base consists of two rectangles:

1. Rectangular part on the left:

   • Width = 5 cm
   • Height = 15 cm
   • Area (A1) = Width × Height = 5 cm × 15 cm = 75 cm²

2. Rectangular part on the right:

   • Width = 20 cm (total width of the L-shape) - 5 cm (width of the left rectangle) = 15 cm
   • Height = 5 cm
   • Area (A2) = Width × Height = 15 cm × 5 cm = 75 cm²

To find the total area of the L-shaped base (B), we combine the areas of both rectangles: \[ B = A1 + A2 = 75 cm² + 75 cm² = 150 cm² \]

Now that we have the area of the base, we can gather the remaining information needed to calculate the volume of the prism:

1. Area of the base, \( B = 150 cm² \)
2. Height of the prism, \( h = 5 cm \)

Now, calculate the volume \( V \): \[ V = B \cdot h = 150 cm² \cdot 5 cm = 750 cm³ \]

In summary:

• Area of the base, \( B = 150 , cm² \)
• Height of the prism, \( h = 5 , cm \)
• Volume of the prism, \( V = 750 , cm³ \)

Fill in the answers accordingly.