Question Video: Finding the Area of a Trapezoid Mathematics

Video Transcript

𝐴𝐵𝐶𝐷 is a trapezoid where the lengths of its parallel bases 𝐴𝐷 and 𝐵𝐶 are 36 centimeters and 48 centimeters, respectively. The length of the perpendicular drawn from 𝐷 to 𝐵𝐶 is 35 centimeters. Find the area of 𝐴𝐵𝐶𝐷, giving your answer to the nearest square centimeter.

In this question, we’re told that 𝐴𝐵𝐶𝐷 is a trapezoid. We can see this from the diagram as we have a pair of parallel sides. So, we know it is a trapezoid. We’re told that the bases 𝐴𝐷 and 𝐵𝐶 are 36 and 48 centimeters, and that’s on the diagram. We’re also told that the perpendicular drawn from 𝐷 to 𝐵𝐶 is 35 centimeters, and that’s also on the diagram. Importantly, it also tells us that the height of this trapezoid is 35 centimeters.

To find the area of 𝐴𝐵𝐶𝐷, we’re going to use the formula to find the area of a trapezoid. This formula tells us that the area of a trapezoid is equal to a half ℎ times 𝑏 sub one plus 𝑏 sub two, where ℎ is the height of the trapezoid and 𝑏 sub one and 𝑏 sub two are the bases or parallel sides of the trapezoid. So to find the area of 𝐴𝐵𝐶𝐷, we plug in the values that we have. The height is 35 centimeters. 𝑏 sub one and be 𝑏 sub two are 36 and 48, and it doesn’t matter which way around these are. So, for the area, we’re calculating a half times 35 times the sum of 36 and 48. We can simplify 36 plus 48 to give us 84.

As it doesn’t matter which way we multiply, it might seem sensible to find half of 84 rather than half of 35. This means we’re working out 35 times 42. Without a calculator, we could work this out as 1,470. And the units here will be square units of square centimeters. We were asked for an answer to the nearest square centimeter, but we have an integer value here, so we don’t need to round. Therefore, 𝐴𝐵𝐶𝐷 has an area of 1,470 square centimeters.