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

$A_{\triangle ADB}=\dfrac{1}{2}\cdot AB\cdot h_D.$

2. The area of the triangle AEB is

$A_{\triangle AEB}=\dfrac{1}{2}\cdot AB\cdot h_E.$

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: $A_{\triangle ABC}=b+a.$