The area of a trapezoid is 102 square centimeters and the lengths of its parallel sides are 15 centimeters and 10 centimetres. What is its height?
Let’s see if we can model what this trapezoid might look like. As it’s a trapezoid, we know that it will have one pair of parallel sides. And we’re told that these two sides are 10 centimeters and 15 centimeters. So we can make the shorter base or the shorter parallel side 10 centimeters and the longer one 15 centimeters.
We’re also told that the area of the trapezoid is 102 square centimeters, and we’re asked to work out the height. In order to do this, we’ll need to recall the formula for the area of a trapezoid, which connects the height and the parallel sides with the area. It can be written as 𝐴, the area, equals half ℎ times 𝑏 sub one plus 𝑏 sub two, where ℎ is the height and 𝑏 sub one and 𝑏 sub two are the lengths of the parallel sides.
We can then take the formula and plug in the values that we’re given. The area is 102. The height, ℎ, is what we wish to find out. And the two parallel sides, 𝑏 sub one and 𝑏 sub two, are 10 and 15. And it doesn’t matter which way round we write these in the formula. Adding together our values in parentheses, we can simplify this to 25.
Then in order to get rid of this fraction of a half on the right-hand side, we can multiply each side of this equation by two. So we’d have 204 equals ℎ times 25 or rather 25ℎ. In order to find the value of ℎ, we can then divide both sides by 25. So we have 204 over 25 equals ℎ. We can work this out without a calculator using a long division method. We’d get the whole-answer part of eight, a remainder of four, which would be written as a fraction over 25.
Whilst this answer is perfectly valid mathematically, we may decide that we wish to write it as a decimal instead. In this case, we can consider that an equivalent fraction to four twenty-fifths would be sixteen hundredths. And so we can give our answer as eight and sixteen hundredths or 8.16. And as this is a length, then the units will be in centimeters.