Video Transcript
Find the area of the quadrilateral, giving the answer to the nearest square unit.
Let’s begin by identifying what type of quadrilateral we’ve been asked to find the
area of. It has been drawn on a square grid, and we can therefore identify that the sides at
the top and bottom are parallel to one another. As this quadrilateral has one pair of parallel sides, it is a trapezoid. We can then recall that the area of a trapezoid is equal to half the sum of the
lengths of its parallel sides multiplied by its height. Using the letters 𝑎 and 𝑏 to denote the lengths of the parallel sides and ℎ to
denote the height, we can write this formula as area of trapezoid equals a half 𝑎
plus 𝑏 multiplied by ℎ.
We can determine the lengths of the parallel sides and the height of the trapezoid by
counting squares on the figure. The parallel side at the top of the figure is 12 units long. The parallel side at the bottom of the figure is 16 units long. And the height of the trapezoid is nine units. Substituting 12 and 16 for the lengths of the parallel sides and nine for the height
gives the area of this trapezoid is equal to a half multiplied by 12 plus 16
multiplied by nine. 12 plus 16 is 28, and half of 28 is 14. So this calculation simplifies to 14 multiplied by nine, which is 126. We’re asked to give the answer to the nearest square unit. But as this value is an integer, no rounding is required.
So, we can conclude that the area of this quadrilateral, which we’ve identified is a
trapezoid, is 126 square units.
