A parallelogram ABCD has an area of 150 $c m^{2}$ . If a diagonal BD is drawn, what is the ratio of the area of $Δ A B D$ and the area of $Δ B C D$ ?

1:1

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1:2

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1:3

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2:1

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Solution

The correct option is A 1:1
Triangles ABD and BCD have equal bases, AB and CD.

Also, since the two triangles are between the same two parallel lines, AB and CD, their heights are equal.

Two equal triangles with equal bases and equal heights have equal areas.

Hence, area of $Δ$ ABD : area of $Δ$ BCD
= 1:1

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A parallelogram ABCD has an area of 150 cm2. If a diagonal BD is drawn, what is the ratio of the area of Δ ABD and the area of Δ BCD?

A parallelogram ABCD has an area of 150 $c m^{2}$ . If a diagonal BD is drawn, what is the ratio of the area of $Δ A B D$ and the area of $Δ B C D$ ?