Question Video: Finding the Length of a Base in a Trapezoid given the Other Base's Length, the Height, and the Area Mathematics

A trapezoid of area 132 and base 20 has height 11. What is the length of the other base?

02:18

Video Transcript

A trapezoid of area 132 and base 20 has height 11. What is the length of the other base?

It might be sensible to start this question by drawing a diagram to model the information. We’re told in this question that we have a trapezoid. We can remember that a trapezoid is a quadrilateral, that’s a four-sided shape, with a pair of parallel sides. The height is 11 units. We’re told that one of the bases is 20, and we need to find the length of the other base. When we talk about bases in trapezoids, that means the lengths of the parallel sides. We don’t know which base is 20 but let’s write it as the lower base.

In order to work out the length of the other base, we’ll need to use the information about the area. In some countries, the word trapezium is used to refer to a shape with one pair of parallel sides. Here, we’re told that the area is 132 square units. And we can use the formula for the area of a trapezium or a trapezoid, which tells us that the area is equal to a half ℎ times 𝑏 sub one plus 𝑏 sub two. ℎ represents the height of the trapezoid, and 𝑏 sub one and 𝑏 sub two are the two bases. So, taking this formula then, we can fill in the fact that the area is 132, the height is 11. And we don’t know one of the bases, so let’s keep that as 𝑏 sub one. And then we add the base of 20.

We can rearrange this equation to find 𝑏 sub one in a number of ways. But let’s start by removing this half by multiplying both sides of the equation by two. 132 multiplied by two gives us 264. And on the right-hand side, we’ll still have 11 times 𝑏 sub one plus 20. We can then divide both sides of the equation by 11. 264 divided by 11 gives us 24. And on the right-hand side then, we’ll have 𝑏 sub one plus 20. We can then find 𝑏 sub one by subtracting 20 from both sides of the equation. And so, our answer is that the other base must have been four units long.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.