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Question

If a and b are the two sides of a triangle, then the area of triangle will be given by |a×b|

A
True
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B
False
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Solution

The correct option is B False

As shown in the figure if a and b represent the two sides of a triangle then the area of triangle is given by 12|a×b| and not a×b
Why is it so?
Look area of a triangle is given by 12(Base) × ( Perpendicular distance of the base from the opposite vertex)
So 12|a×b|=12(|a||b|sinϕ) whereϕ is the angle between a and b
Now |b| sinϕ will be nothing but the perpendicular distance of a from the opposite vertex)
So, 12(|a||b|sinϕ)=12(|a|) x perpendicular distance of a from the opposite vertex)
Which is nothing but the area of the triangle.

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