Use the model for the base of a triangular prism and a triangular pyramid. if the heights are both 9 cm, what is the volume of each shape?
the images shows a triangle with a dotted line down the middle and 6 cm at the bottom and 4cm next to the dotted line
To find the volume of each shape, we first need to calculate the area of the base triangle.
The area of a triangle can be found using the formula A = 0.5 * base * height.
For the base triangle in this case, the base is 6 cm and the height is 4 cm.
A = 0.5 * 6 cm * 4 cm = 12 cm^2.
Now, let's calculate the volume of each shape:
Volume of a triangular prism = base area * height
Volume of triangular prism = 12 cm^2 * 9 cm = 108 cm^3
Volume of a triangular pyramid = 1/3 * base area * height
Volume of triangular pyramid = 1/3 * 12 cm^2 * 9 cm = 36 cm^3
Therefore, the volume of the triangular prism is 108 cm^3 and the volume of the triangular pyramid is 36 cm^3.