Video Transcript
Given that the area of the
parallelogram 𝐴𝐵𝐶𝐷 is equal to 268 square centimeters, find the area of triangle
𝑋𝐵𝐶.
We are told in the question that
the area of the parallelogram is 268 square centimeters. We recall that the area of a
parallelogram is equal to the base multiplied by the perpendicular height. In this question, however, we’re
not given either of these dimensions. We do know, however, that the area
of any triangle is equal to the base multiplied by its height divided by two. Once again, this height must be the
perpendicular height.
In the figure drawn, the
parallelogram and triangle share a base, the length 𝐵𝐶. They also share the same
perpendicular height, the length 𝑋𝑀, as shown on the diagram. As the area of the parallelogram is
base multiplied by height and the area of the triangle is base multiplied by height
divided by two, the triangle must have half the area of the parallelogram. The area of triangle 𝑋𝐵𝐶 is
therefore equal to 268 divided by two or half of 268. This is equal to 134. We can therefore conclude that the
area of triangle 𝑋𝐵𝐶 is equal to 134 square centimeters.
