Question

In triangle ABC, AM is a median. A line drawn through point M intersects AB at its midpoint P. Find the areas of triangles APC and PMC if the area of APM is 35 m².

a. 17.5 m² and 17.5 m²
b. 35 m² and 0 m²
c. 70 m² and 35 m²
d. 0 m² and 35 m²

Answer 1

The areas of triangles APC and PMC are both 17.5 m².

Step-by-step explanation:

To find the areas of triangles APC and PMC, we need to use the fact that the line drawn through point M intersects AB at its midpoint P. Since AM is a median, it divides the triangle ABC into two congruent triangles. Therefore, the area of triangle APC is equal to half the area of triangle APM, which is half of 35 m². So, the area of triangle APC is 17.5 m².

Similarly, the area of triangle PMC is also 17.5 m². Therefore, the correct answer is option a. 17.5 m² and 17.5 m².