 1800-212-7858 (Toll Free)
9:00am - 8:00pm IST all days
8104911739

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

022-62211530

Mon to Sat - 11 AM to 8 PM

D, E and F respectively are the mid-points of the sides BC, CA and AB of ABC. Show that ar( DEF) = Asked by Topperlearning User 4th June 2014, 1:23 PM D and E are mid points of BC and AC. DE||AB and DE = (Mid-point Theorem)

Similarly, E and F are mid points of AC and AB. EF||BC and EF = In quadrilateral BDEF, DE||BF and FE||BD BDEF is a parallelogram

Similarly, DCEF and AFDE are parallelograms.

We know that diagonal of a parallelogram divides it into two triangles of equal area. Area ( BFD) = Area ( DEF) (For parallelogram BDEF)

Area ( CDE) = Area ( DEF) (For parallelogram DCEF)

Area ( AFE) = Area ( DEF) (For parallelogram AFDE) Area ( AFE) = Area ( BFD) = Area ( CDE) = Area ( DEF)

Also,

Area ( AFE) + Area ( BDF) + Area ( CDE) + Area ( DEF) = Area ( ABC) Area ( DEF) + Area ( DEF) + Area ( DEF) + Area ( DEF) = Area ( ABC) 4 Area ( DEF) = Area ( ABC) Area ( DEF) = Area ( ABC)

Answered by Expert 4th June 2014, 3:23 PM
• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10

You have rated this answer /10

RELATED STUDY RESOURCES :  