Question Video: Finding the Area of a Trapezoid Given the Length of Its Middle Base and Height Mathematics

Video Transcript

Find the area of the shown trapezoid.

Let’s look more closely at the figure to identify what information we’ve been given. The two parallel sides of the trapezoid are 𝐴𝐵 and 𝐷𝐶. But we haven’t been given the lengths of either of these sides. We have been given the perpendicular distance between these sides, the trapezoid’s height, which is eight millimeters.

The other length we’ve been given is the length of a line segment in the interior of the trapezoid. This line segment connects the points 𝑋 and 𝑌, which lie on the legs of the trapezoid.

We can see that line segments 𝐴𝑋 and 𝐷𝑋 are of equal length, and so 𝑋 is the midpoint of side 𝐴𝐷. In the same way, line segments 𝐵𝑌 and 𝐶𝑌 are of equal length, so 𝑌 is the midpoint of the side 𝐵𝐶. This means that 𝑋𝑌 is the middle base of the trapezoid.

The middle base is defined as being the line segment whose endpoints are the midpoints of the legs of a trapezoid. This is helpful because there is a formula for calculating the area of a trapezoid using the length of its middle base and its height. The area is simply equal to the length of the middle base multiplied by the height.

So, the area of trapezoid 𝐴𝐵𝐶𝐷 is equal to 19 multiplied by eight, which is 152. The units for this area are square millimeters. So by identifying that the line segment 𝑋𝑌 is the middle base of the given trapezoid, we found that its area is 152 square millimeters.