Question

In triangle ABC, AM is a median (ME = BC). A line drawn through point M intersects AB at its midpoint P. Find the areas of AAPC and APMC if the area of triangle ABC is 35 m².

Answer 1

The areas of triangles AAPC and APMC are both 17.5 m² since AM is a median dividing triangle ABC into two equal areas and AP is a median of AAPC dividing it into two equal areas.

Step-by-step explanation:

In triangle ABC, AM is a median, meaning AM divides the area of triangle ABC into two equal parts. Since we are told that the area of triangle ABC is 35 m², this means the area of triangle AMC is half of that, so it is 17.5 m². As the line through point M intersects AB at its midpoint P, AP is half the length of AB, and since AM is the median, AP is also the median of triangle AAP, therefore, AAP and APM have the same area. Consequently, triangles AAPC and APMC both have an area of 17.5 m².