P is any point on base BC of ΔABC and D is the mid-point of BC. DE is drawn parallel to PA to meet AC at E. If then find area of ΔEPC.

Question

P is any point on base BC of &#x394;ABC and D is the mid-point of BC. DE is drawn parallel to PA to meet AC at E. If then find area of &#x394;EPC.

Philoid · Accepted Answer

Given that,

Area ( = 12 cm²

D is the mid-point of BC

So,

AD is the median of triangle ABC,

Area ( = Area ( = * Area (

Area ( = Area ( = * 12

= 6 cm² (i)

We know that,

Area of triangle between the same parallel and on the same base

Area ( = Area (

Area ( + Area ( = Area ( + Area (

Area ( = Area ( (ii)

ME is the median of triangle ADC,

Area ( = Area ( + Area (

Area ( = Area ( + Area ( [From (ii)]

Area ( = Area (

6 cm² = Area ( [From (i)]

Hence,

Area ( is 6 cm².