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

# If a triangle and a parallelogram are on the same base and between the same parallels, then

A

area of triangle = (1/4) area of parallelogram

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

area of triangle = (1/3)area of parallelogram

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

area of triangle = (1/2)area of parallelogram

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

area of triangle = area of parallelogram

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C area of triangle = (1/2)area of parallelogram Let △ABP and parallelogram ABCD be on the same base AB and between the same parallels AB and PC. To prove that, ar (△PAB) = 12 x ar (ABCD) Draw BQ parallel to AP to obtain another parallelogram ABQP. Now parallelograms ABQP and ABCD are on the same base AB and between the same parallels AB and PC. Therefore, ar (ABQP) = ar (ABCD) But △PAB ≅ △BQP [Diagonal PB divides parallelogram ABQP into two congruent triangles] So, ar(△PAB)=ar(△BQP) Therefore, ar (△PAB) = 12 ar (ABQP) This gives ar (△PAB) = 12 ar (ABCD)

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Parallelograms on the Same Base and between the Same Parallels Are Equal in Area
MATHEMATICS
Watch in App
Join BYJU'S Learning Program