Question

P is any point on base BC of ΔABC and D is the mid-point of BC. DE is drawn parallel toPA to meet AC at E. If ar (ΔABC) = 12 cm², then find area of ΔEPC. 

Answer 1

Given: Area (ABC) = 12 cm², D is midpoint of BC and AP is parallel to ED. We need to find area of the triangle EPC. 

Since, AP||ED, and we know that the area of triangles between the same parallel and on the same base are equal. So,

Area (APE) = Area (APD)

⇒ Area (APM) + Area (AME) = Area (APM) + Area (PMD)

⇒ Area (AME) = Area (PMD) …… (1)

Since, median divide triangles into two equal parts. So,

Area (ADC) = `1/2` Area (ABC) = `12/2`  = 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.