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Triangles on the Same Base (Or Equal Bases) and Equal Areas Will Lie between the Same Parallels

If a triangle...

Question

If a triangle and a parallelogram are on the same base and between the same parallels, then _____.

area of triangle = $\frac{1}{4} \times a r e a o f p a r a l l e l o g r a m$

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area of triangle = $\frac{1}{3} \times a r e a o f p a r a l l e l o g r a m$

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area of triangle = $\frac{1}{2} \times a r e a o f p a r a l l e l o g r a m$

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area of triangle = area of parallelogram

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Solution

The correct option is C
area of triangle = $\frac{1}{2} \times a r e a o f p a r a l l e l o g r a m$

Let $△ A B P$ and parallelogram ABCD be on the same base AB and between the same parallels AB and PC. Let h be the height of the triangle and the parallelogram.
Area of $△ P A B = \frac{1}{2} \times A B \times h$
$A r e a o f p a r a l l e l o g r a m A B C D = A B \times h$
$A r e a (△ P A B) = \frac{1}{2} \times a r e a o f p a r a l l e l o g r a m A B C D .$

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