Question Video: Finding Triangles of Equal Areas Mathematics • Second Year of Preparatory School

Video Transcript

Given that the area of triangle 𝐵𝐷𝐸 equals 63 square centimeters, find the area of triangle 𝐶𝐷𝐸.

Observe that segments 𝐴𝐷 and 𝐷𝐵 are congruent and lie on the same line. Furthermore, triangles 𝐵𝐷𝐸 and 𝐴𝐷𝐸 share a common vertex at 𝐸. It follows that they have the same area. Similarly, triangles 𝐴𝐷𝐸 and 𝐶𝐷𝐸 have congruent bases and share a common vertex at 𝐷. It follows that triangles 𝐶𝐷𝐸, 𝐴𝐷𝐸, and 𝐵𝐷𝐸 all have the same area, which is 63 square centimeters.