Question

The volume of both of these trapezoidal prisms is 24 cubic units. Their heights are 6 and 8 units, as labeled. What is the area of a trapezoidal base of each prism?

A
units2
B
units2

Answer 1

A = 4 units squared

B = 3 units squared

Explanation:

A lot of volume questions can be answered by finding the area of the base, and multiplying it by the height. This does not work with shapes that are not prisms, such as a sphere or cone.

First, we know that both prism's have an area of 24 cubic units. Since we know that in prisms, to find their volume, all we need to do is multiply the height and the area of the base, we can set up an equation. The variable 'x' can represent what we do not know (the area of the base). Equation for A:

A: x * 6 = 24

Now, we need to figure out what multiples by 6 to get to 24. To do this, we can divide 24 by 6. We get:

A: x = 4

Using the same reasoning used in figure A, this is the equation for B:

B: x * 8 = 24

Now, we need to figure out what multiplies by 8 to get to 24. To do this, we can divide 24 by 8. We get:

B: x = 3

* * NOTE: THE 'x' does not have the same value in both situations. We used x to represent the area of the base in both situations. * *