Question

prove that area of a triangle =1/2*base*height​

Answer 1

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Answer 2

Solution :

GIVEN : A ∆ABC in which BC is the base and AL is the corresponding height.

TO PROVE : ar(∆ABC) = 1/2×BC×AL.

CONSTRUCTION : Through A and C, draw AD || BC & CD || BA , intersecting each other at D.

PROOF : AD || BC & CD || BA ➨ BCDA is a ||gm.

Thus , BCDA is a ||gm whose diagonal AC divides it into two triangles of equal areas.

Hence , ar(∆ABC) = 1/2×ar(||gm BCDA)

➨ 1/2 × BC × AL ( Since , ar(||gm BCDA = BC × AL )

Hence , Area of triangle = 1/2 × base × height.