Which of the following triangles is half the area of parallelogram PAIN.

Δ A I N

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Δ D I P

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Δ P I N

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Δ A I P

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Solution

The correct options are
A $Δ A I N$
C $Δ P I N$
D $Δ A I P$
If a triangle and a parallelogram are on the same base and between the same parallel lines, the area of the triangle is equal to half the area of the parallelogram.
$Δ A I N, Δ P I N, Δ A I P, Δ P A N$
and parallelogram PAIN are on the same base and between the same parallel lines.
$∴ a r (Δ A I N) = a r (Δ P I N) = a r (Δ A I P) = \frac{1}{2} a r (P A I N)$

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If a parallelogram and a triangle are on the same base and between the same parallels, then the area of triangle is half the area of parallelogram.

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