The area of a trapezium is 1900. If one of its parallel sides is 50 and its height is 50, what is the length of the other parallel side?
A trapezium is a quadrilateral with exactly one pair of parallel sides. And we will show the sides to be parallel using arrows. And the formula to find the area of a trapezium is one-half times the height times the bases added together — 𝑏 one plus 𝑏 two. So before we begin plugging into the formula, let’s go ahead and label our picture.
We begin with knowing that the area is equal to 1900 and one of its parallel sides is 50. So we could have picked either one. And then, we also know that the height is 50, which we’ve labelled here. So let’s begin plugging into the formula so that way we can find the length of the other parallel side. So we need to plug in 1900 for the area, 50 for the height, and 50 for one of the bases. We will plug 50 in for 𝑏 one. So this means we are solving for 𝑏 two — the other base, which is the other parallel side that we’re trying to find the length of. So this would be considered base one.
So in order to solve for 𝑏 two, let’s go ahead and multiply one-half times 50, which is equal to 25. Now, we need to divide both sides of this equation by 25. The 25s cancel on the right and we get 76 on the left. So now to solve for 𝑏 two, we need to subtract 50 from both sides of the equation. So we get that 𝑏 two is equal to 26.
Therefore, the length of the other parallel side is equal to 26.