To find the volume of a triangular prism, you need to multiply the area of the base (which is a triangle) by the height. The formula is: V = (1/2) * base * height * height.
For the triangular prism:
V = (1/2) * 4 * 6 * 9
V = (1/2) * 24 * 9
V = 12 * 9
V = 108 cm^3
For the triangular pyramid, you also multiply the area of the base by the height and then divide by 3. The formula is: V = (1/3) * base * height.
For the triangular pyramid:
V = (1/3) * 4 * 6 * 9
V = (1/3) * 24 * 9
V = 8 * 9
V = 72 cm^3
Therefore, the volume of the triangular prism is 108 cm^3 and the volume of the triangular pyramid is 72 cm^3.
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Use the model for the base of a triangular prism and triangular pyramid. If the heights are both 9 cm, what is the volume of each shape?
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O prism: 36 cm'; pyramid: 108 cm' O prism: 108 cm*; pyramid: 36 cm₴
• prism: 72 cm"; pyramid: 216 cm*
• prism: 216 cm"; pyramid: 72 cm?
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