The given rectangular prism and triangular prism have the same height, h. The rectangular prism has a cross section that is a rectangle with a length of 6 inches and a width of 5 inches. The triangular prism has a cross section that is a triangle with a base of 12 inches and a height of 5 inches. Compare the volume of the two prisms.
Accepted Solution
A:
The shapes will have the same volume.
To find the volume of a prism, we just need to multiply the area of the base by the height. In his case, they have the same heights. To determine which is bigger, therefore we just need to compare the areas of the bases.
In a prism, the cross section of the shape will be the same as the base.
Area of the cross sections: Rectangle: 6 x 5 = 30 Triangle: 12 x 5 / 2 = 30
Since the bases are the same, the volume will be the same.