Question

AM is a median in △ABC (M∈ BC ). A line drawn through point M intersects AB at its midpoint P. Find areas of △APC and △PMC, if Area of APM=35m^2.

Answer 1

Answer: Area of ΔAPC = 70 square meter and Area of △PMC= 35 square meter

Step-by-step explanation:

Here, AM is a median in △ABC (M∈ BC ). A line drawn through point M intersects AB at its midpoint P.

Since, we know that median divides a triangle into equal areas.

Therefore, By the diagram we can say that If Area of ΔAPM=35 $m^2$.

Therefore Area of ΔBPM = 35 ( Because MP is the median of triangle MAB.)

⇒ Area of ΔPMC = 35 ( Because MP is the median of triangle PBC.)

Now, Area of ΔAPC= Area of ΔPBC ( CP is the median of ΔABC)

But area of ΔPBC= Area of ΔBPM+ area of ΔPMC= 35+35=70 square unit.

⇒ Area of  Δ APC= 70 square unit.