Final answer:
To find the areas of triangles APC and PMC, use the formula: Area = (1/2) * base * height. The base for both triangles is half the length of AB, and the height for triangle APC is AM and for triangle PMC is MC.
Step-by-step explanation:
In triangle ABC, if AM is a median and a line drawn through point M intersects AB at its midpoint P, we can find the areas of triangles APC and PMC. Given that A = 35m, we need to calculate the areas of these triangles.
To find the area of triangle APC, we can use the formula:
Area = (1/2) * base * height
The base is AP, which is half the length of AB since P is the midpoint. The height is the distance from point C to line AP, which is AM since AM is a median. So, the area of triangle APC is (1/2) * (AB/2) * AM.
To find the area of triangle PMC, we can use the same formula:
Area = (1/2) * base * height
The base is PM, which is half the length of AB since P is the midpoint. The height is the distance from point C to line PM, which is MC. So, the area of triangle PMC is (1/2) * (AB/2) * MC.