If the area of parallelogram ABCD is 54 square units, what is the area of parallelogram ABEF? [Given: O and P are the midpoints of AD and BC respectively]

27 square units

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30 square units

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33 square units

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36 square units

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Solution

The correct option is A
27 square units

O and P are the midpoints of AD and AC respectively.

$S o, F R = \frac{D Q}{2}$

Also, AB || CD and AB || EF. This implies that EF || CD.

Area of ABCD = $A B \times D Q$

Area of $A B E F = A B \times F R = A B \times (\frac{D Q}{2}) = \frac{1}{2} \times (A r e a o f A B C D) = \frac{1}{2} \times 54 = 27$ square units.

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If the area of parallelogram ABCD is 54 square units, what is the area of parallelogram ABEF? [Given: O and P are the midpoints of AD and BC respectively]

The correct option is A 27 square units O and P are the midpoints of AD and AC respectively. So, FR=DQ2 Also, AB || CD and AB || EF. This implies that EF || CD. Area of ABCD = AB×DQ Area of ABEF=AB×FR=AB×(DQ2)=12×(Area of ABCD)=12×54=27 square units.