Problem Analysis
The image shows six triangular prisms, and the task is likely to calculate the
volume of each prism. The formula for the volume of a triangular prism is:
\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]
For a triangular prism, the base is a triangle, so the base area is calculated using the formula for the area of a triangle:
\[
\text{Base Area} = \frac{1}{2} \times \text{base of triangle} \times \text{height of triangle}
\]
The height of the prism is the length perpendicular to the triangular base.
Step-by-Step Solution
#### Prism 1:
-
Base of triangle: 5 cm
-
Height of triangle: 6 cm
-
Height of prism: 5 cm
1. Calculate the base area:
\[
\text{Base Area} = \frac{1}{2} \times 5 \times 6 = 15 \, \text{cm}^2
\]
2. Calculate the volume:
\[
\text{Volume} = \text{Base Area} \times \text{Height of prism} = 15 \times 5 = 75 \, \text{cm}^3
\]
#### Prism 2:
-
Base of triangle: 5 cm
-
Height of triangle: 6 cm
-
Height of prism: 6 cm
1. Calculate the base area:
\[
\text{Base Area} = \frac{1}{2} \times 5 \times 6 = 15 \, \text{cm}^2
\]
2. Calculate the volume:
\[
\text{Volume} = \text{Base Area} \times \text{Height of prism} = 15 \times 6 = 90 \, \text{cm}^3
\]
#### Prism 3:
-
Base of triangle: 15 cm
-
Height of triangle: 6 cm
-
Height of prism: 5 cm
1. Calculate the base area:
\[
\text{Base Area} = \frac{1}{2} \times 15 \times 6 = 45 \, \text{cm}^2
\]
2. Calculate the volume:
\[
\text{Volume} = \text{Base Area} \times \text{Height of prism} = 45 \times 5 = 225 \, \text{cm}^3
\]
#### Prism 4:
-
Base of triangle: 2.5 cm
-
Height of triangle: 3 cm
-
Height of prism: 7.5 cm
1. Calculate the base area:
\[
\text{Base Area} = \frac{1}{2} \times 2.5 \times 3 = 3.75 \, \text{cm}^2
\]
2. Calculate the volume:
\[
\text{Volume} = \text{Base Area} \times \text{Height of prism} = 3.75 \times 7.5 = 28.125 \, \text{cm}^3
\]
#### Prism 5:
-
Base of triangle: 5 cm
-
Height of triangle: 6 cm
-
Height of prism: 15 cm
1. Calculate the base area:
\[
\text{Base Area} = \frac{1}{2} \times 5 \times 6 = 15 \, \text{cm}^2
\]
2. Calculate the volume:
\[
\text{Volume} = \text{Base Area} \times \text{Height of prism} = 15 \times 15 = 225 \, \text{cm}^3
\]
#### Prism 6:
-
Base of triangle: 25 cm
-
Height of triangle: 30 cm
-
Height of prism: 7.5 cm
1. Calculate the base area:
\[
\text{Base Area} = \frac{1}{2} \times 25 \times 30 = 375 \, \text{cm}^2
\]
2. Calculate the volume:
\[
\text{Volume} = \text{Base Area} \times \text{Height of prism} = 375 \times 7.5 = 2812.5 \, \text{cm}^3
\]
Final Answer
The volumes of the prisms are:
\[
\boxed{75, 90, 225, 28.125, 225, 2812.5}
\]
Parent Tip: Review the logic above to help your child master the concept of pyramid volume worksheet.
