Question

prove that the area of a triangle is half the product of any of its sides and the corresponding altitude

Answer 1

area of triangle=1/2×base×height

Answer 2

▪♥HELLO MATE♥▪
here is your answer...

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GIVEN : ΔABC, in which AL is altitude to Side BC

TO PROVE : ar(ΔABC) = ½(BC × AL)

CONSTRUCTION : Draw CD || BA and AD || BC through C and A respectively, let they intersect at point D.

PROOF : We have, BA || CD (by construction)
and AD || BC (by contraction)
Therefore, ABCD is a parallelogram.
Since, AC is diagonal of parallelogram ABCD
Therefore, ar(ΔABC) = ½ ar( ||gm ABCD) [ diagonal of parallelogram divide it into two triangles of equal areas ]
= ½ (BC × AL)
[ Area of parallelogram is product of base and corresponding altitudes ]

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