Video Transcript
Which triangle has the same area as triangle πππΎ?
Triangle πππΎ is found here. The area of a triangle is equal to one-half times the base times the height. So letβs look at the base of each triangle. The base will run on the parallel lines, because the base doesnβt necessarily mean the bottom. We can choose any side, but we have to be careful and make sure that the height is perpendicular to it.
So here is the base of ππ, here is the base of πΆπ, and hereβs the base of ππ·. Notice that all three of the bases are congruent. So right now, any of the three triangles could work. So what about the height? The heights that would be the same as triangle πππΎ would then have the same area as triangle πππΎ, because they already have the same base.
The height of triangle πππΎ would be here; itβs the distance between the parallel lines. The height of triangle πΆππ» is found here; itβs the distance between the parallel lines. And itβs the exact same for the last triangle. So they all have the same base, and they all have the same height. That means their areas would all be equal.
So which triangle has the same area as triangle πππΎ? It would be either triangle πΆππ» or triangle ππ·π, because if two triangles with equal base links lie between two parallel straight lines, then the triangles are equal in area.