Get a free home demo of LearnNext

Available for CBSE, ICSE and State Board syllabus.
Call our LearnNext Expert on 1800 419 1234 (tollfree)
OR submit details below for a call back


Areas of Triangles

Have a doubt? Clear it now.
live_help Have a doubt, Ask our Expert Ask Now
format_list_bulleted Take this Lesson Test Start Test

Areas of Triangles - Lesson Summary

Two triangles on the same base or equal bases and between the same parallels are equal in area.

Given  : Triangles ΔABC and ΔABD are on a common base AB and between same parallels AB and CD.

To Prove : ar(ΔABC) = ar(ΔABD)

Construction : Draw BL||AC , BM||AD

Proof : ABLC is a parallelogram
           (∴ AC||BL and AB||CL)
          ABMD is a parallelogram
           (∴ AD||BM and AB||DM)

   ar(||gm ABLC) = ar(||gm ABMD) ..........(1)
In (||gm ABLC) , ar(ΔABC) = ar (ΔCLB)

∴ar(||gm ABLC) = 2ar(ΔABC) ..........(2)

In (||gm ABMD) , ar(ΔABD) = ar (ΔBDM)
∴ar(||gm ABMD) = 2ar(ΔABD) ..........(3)
     2ar(ΔABC) = 2 ar(ΔABD)..........(4)
⇒ ar(ΔABC) = ar(ΔABD)

Area of a triangle is half the product of its base and the corresponding altitude.

Median of a triangle divides it into two triangles of equal area.

Two triangles with same base (or equal bases) and equal areas will have equal corresponding altitudes.

Triangles on the same base and having equal areas lie between the same parallels.

If triangles ABC and ABD are on a common base AB and ar( ABC) = ar( ABD), then AB || CD.

Diagonals of a parallelogram divide it into four triangles of equal area.


Feel the LearnNext Experience on App

Download app, watch sample animated video lessons and get a free trial.

Desktop Download Now
Try LearnNext at home

Get a free home demo. Book an appointment now!