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Question
ABCD is a quadrilateral and BD is one of its diagonals as shown in the following figure. Find the area of quadrilateral ABCD.
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Solution
The correct option is B 12 square units
From the figure it is clear that, ∠CDB=∠ABD=90∘
Also, DC=AB=3 units (From figure)
Now, we know that a quadrilateral is a parallelogram if a pair of opposite sides is parallel and is of equal length.
∴ Quadrilateral ABCD is a parallelogram.
Now, area of the ||gm ABCD
=Base×Corresponding altitude
=AB×BD
=3×4 square units
=12 square units
From the figure it is clear that, ∠CDB=∠ABD=90∘
Also, DC=AB=3 units (From figure)
Now, we know that a quadrilateral is a parallelogram if a pair of opposite sides is parallel and is of equal length.
∴ Quadrilateral ABCD is a parallelogram.
Now, area of the ||gm ABCD
=Base×Corresponding altitude
=AB×BD
=3×4 square units
=12 square units
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