Question

In the following figure, AP ⊥ BC, AD || BC, then find A(∆ABC): A(∆BCD). 

Answer 1

Formula for a triangle:

`A = 1/2 xx ` base × height

Use geometric observations

BC is common base for both triangles
For △ABC, height is AP
For △BCD, since AD∥BC, the height from D to BC is equal to height from A to BC (i.e., same as AP)

BUT the triangle ABC only spans from A to C, while △BCD spans from D to C, depending on the full coordinates or positions, we need to visually estimate the areas.

From the figure:

• Point A is vertically above point PPP, with P ∈ BC

• Triangle ABC is left of diagonal AD

• Triangle BCD is right of diagonal AD

From symmetry, it appears:

A(∆ABC) = A(∆BCD)

`(A(ΔABC))/(A(ΔBCD)) = 1:1`