Video Transcript
This trapezoid’s area is 30,000
square yards. What is its height?
We’ve been given the area of this
trapezoid, so let’s begin by recalling how this is calculated. A trapezoid is characterized by
having one pair of parallel sides. Its area is equal to half the sum
of the lengths of these parallel sides multiplied by its height. We often use the letters 𝑎 and 𝑏
to denote the lengths of the parallel sides and ℎ to denote the height. And then the formula can be written
as a half 𝑎 plus 𝑏 multiplied by ℎ.
In the trapezoid shown, we can
identify that the parallel sides are the two horizontal sides, which have lengths of
80 and 295 yards. The other length given, 232 yards,
is the length of one of the nonparallel sides, which we call the legs of the
trapezoid. We don’t need to use this value in
answering the question.
We’re also given the area of the
trapezoid, so we can substitute this value and the lengths of the two parallel sides
into the area formula to give an equation which we’ll be able to solve to calculate
the height. Substituting these values gives
30,000 equals a half 80 plus 295 multiplied by ℎ. To simplify the equation, we can
multiply both sides by two and also evaluate 80 plus 295. The equation becomes 60,000 equals
375ℎ. To solve for ℎ, we divide both
sides of the equation by 375, giving ℎ equals 60,000 over 375. This simplifies exactly to 160.
So by recalling the formula for
calculating the area of a trapezoid and using this to form and solve an equation,
we’ve found that the height of this trapezoid is 160 yards.
