Q. 24.5( 4 Votes )

If any triangle and any parallelogram are on the same base and between same parallels let us prove logically that the area of triangular region is half the area in the shape of parallelogram region.

Answer :

Given.


If any triangle and parallelogram are on the same base and between the same parallel.


Formula used.


Area of parallelogram = Base × Perpendicular


Area of triangle = × Base × Height


Property of parallel lines


Perpendicular distance between 2 parallel is always same.


Draw a parallelogram ABCD between 2 parallel lines PQ and RS


Draw triangle with base CD and point E on common line AB



As we know that if both parallelogram and triangle lies on same 2 parallel lines


Perpendicular height of both will be same


Height of triangle(EF) = perpendicular of parallelogram (AG)


By Property of parallel lines


As both parallelogram and triangle possess same base CD


Which is also Base of parallelogram


Base of parallelogram = Base of triangle = CD


Area of triangle = × Base × Height


× CD × EF


× CD × AG EF = AG


× [Perpendicular × Base of parallelogram]


× [Area of Parallelogram]


Hence proved;


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Master Theorems in CirclesMaster Theorems in CirclesMaster Theorems in Circles42 mins
Quiz | Area and ParallelogramQuiz | Area and ParallelogramQuiz | Area and Parallelogram46 mins
Champ Quiz | Area of TriangleChamp Quiz | Area of TriangleChamp Quiz | Area of Triangle53 mins
Quiz | Surface Area & VolumesQuiz | Surface Area & VolumesQuiz | Surface Area & Volumes49 mins
Surface Area of Right Circular CylinderSurface Area of Right Circular CylinderSurface Area of Right Circular Cylinder52 mins
Quiz | MensurationQuiz | MensurationQuiz | Mensuration42 mins
Champ Quiz | Area of ParallelogramChamp Quiz | Area of ParallelogramChamp Quiz | Area of Parallelogram55 mins
Proof of Important Theorems of CirclesProof of Important Theorems of CirclesProof of Important Theorems of Circles45 mins
Proof of Important Theorems of CirclesProof of Important Theorems of CirclesProof of Important Theorems of Circles46 mins
Smart Revision | Surface Area and Volume of CubeSmart Revision | Surface Area and Volume of CubeSmart Revision | Surface Area and Volume of Cube40 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :