1. Volume of Triangular Prisms and Pyramids
10.2
Volume of Triangular Prisms and Pyramids
How do you find the volume of a triangular prism or a triangular pyramid?

2. ADDITIONAL EXAMPLE 1
Find the volume of the triangular prism.
3,510 m3

3. ADDITIONAL EXAMPLE 2
Two plastic geometric models shaped like a triangular prism and a triangular pyramid are each 16 cm tall. The base of each model is a triangle with a base of 12 cm and a height of 5 cm. How much greater than the volume of the pyramid is the volume of the prism?
320 cm3 greater

4. 10.2 LESSON QUIZ 1. Find the volume of the triangular prism. 3,159 mm3

5. 2.
A triangular prism and a triangular pyramid have congruent bases with an area of 25 ft2. They both have a height of 15 ft. Find the volume of each figure.
prism: 375 ft3; pyramid: 125 ft3 3.
A block is shaped like a triangular pyramid. The triangular base of the block has a height of 5.2 cm and a base length of 6 cm. If the height of the block is 6.7 cm, what is the volume of the block?
34.84 cm3

6. 4.
A triangular prism and a triangular pyramid have congruent bases. The height of each base is 6 in. The length of each base is 7.5 in. Each figure is 10 in. high. How much greater than the volume of the pyramid is the volume of the prism?
150 in3 greater

7. You have encountered two-dimensional composite figures and found their total area. The figures below are three-dimensional composite solids. You find their total volume in a similar way; find the volume of each simpler solid and then add the results to obtain the total volume. Find the volume of each composite solid. a.
12,348 cm3

8. b.
2,880 ft3

9. How do you find the volume of a triangular prism or a triangular pyramid?
Sample answer:
For both figures, find the area of the base. Then, multiply the area of the prism’s base by the prism’s height. For the pyramid, multiply the area of the base by its height and then by .