1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# In ΔABC, D, E and F are midpoints of BC, AC and AB. If area of parallelogram BDEF is 20 cm2, then the area of ΔABC is equal to:

A
10 cm2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
20 cm2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
40 cm2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
80 cm2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C 40 cm2As we know, on joining the mid-points of the three sides of any triangle will give four congruent triangles. Here, in the given figure D, E and F are midpoints of BC, AC and AB. So, ΔAFE, ΔBDF, ΔFDE, ΔDCE are congruent to each other. Area of parallelogram BDEF =20 cm2 [given] ⇒ Area of ΔBDF + Area of ΔFDE=20 cm2 Since, Area of ΔBDF = Area of ΔFDE ⇒2×Area of ΔBDF =20 cm2 ⇒Area of ΔBDF =10 cm2 Since, ΔAFE, ΔBDF, ΔFDE, ΔDCE are congruent to each other ⇒Area of ΔBDF = Area of ΔFDE = Area of ΔDCE = Area of ΔAFE ⇒Area of ΔABC =4×Area of ΔBDF =4×10 cm2 =40 cm2 ∴ Area of ΔABC =40 cm2

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Area of triangle
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program