Question -
Answer -
Given: Area (ABC) = 12 cm2,D is midpoint of BC and AP is parallel to ED. We need to find area of thetriangle EPC.
Since, AP||ED, and weknow that the area of triangles between the same parallel and on the same baseare equal. So,
Area (APE) = Area (APD)
⇒ Area (APM) + Area (AME) = Area (APM) + Area(PMD)
⇒ Area (AME) = Area (PMD) …… (1)
Since, median dividetriangles into two equal parts. So,
Area (ADC) = 
Area (ABC) = 
= 6 cm2
⇒ Area (ADC) = Area (MDCE) + Area (AME)
⇒Area (ADC) = Area(MDCE) + Area (PMD) (from equation (1))
⇒ Area (ADC) = Area (PEC)
Therefore,
Area (PEC) = 6 cm2.