Question

Line p, parallel to the side AB of △ABC, intersects AC and BC at points D and E respectively. Find the area of △ABC, if AABD=a and AAEC=b.

Answer 1

Consider triangles ADB and AEB.

1. The area of the triangle ADB is

`A_(\triangle ADB)=(1)/(2)\cdot AB\cdot h_D.`

2. The area of the triangle AEB is

`A_(\triangle AEB)=(1)/(2)\cdot AB\cdot h_E.`

3. Since AB and p are parallel lines, then

`h_D=h_E.`

This gives you that

`A_(\triangle ADB)=A_(\triangle AEB)=a.`

Therefore,

`A_(\triangle ABC)=A_(\triangle ACE)+A_(\triangle AEB)=b+a.`

Answer:
`A_(\triangle ABC)=b+a.`