In the adjoining figure, show that ABCD is parallelogram. Calculate the area of parallelogram ABCD.

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Filo · Accepted Answer

Construct AM⊥DC and CL⊥AB. Extended the lines DC and join AC. We know thatArea of the quadrilateral ABCD=area of triangle ABD+ area of triangle DCBFrom the figure we know that Area of △ABD= Area of △DCBso it can be written as Area of the quadrilateral ABCD=2 ( Area of △ABD)We getArea of △ABD=21​ ( area of quadrilateral ABCD )......(1)Area of a quadrilateral ABCD=area of △ABC + area of △CDA.From the figure we know that Area of △ABC=Area of △CDAso it can be written asArea of the quadrilateral ABCD=2 ( Area of △ABC)We getArea of △ABC=21​ ( area of quadrilateral ABCD)......(2)Using the equation (1) and (2)Area of △ABD= Area of △ABC=21​ ( area of quadrilateral ABCD)......(2)Using the equations (1) and (2)Area of △ABD=Area of △ABC=21​BD=21​CLIt can be written asCL=BDIn the same way we getDC=AB and AD=BCHence, ABCD is a parallelogramArea of parallelogram ABCD=base×height=5×7=35 cm2Therefore, area of parallelogram ABCD is 35 cm2.

Question Text	In the adjoining figure, show that $A BC D$ is parallelogram. Calculate the area of parallelogram $A BC D$ .
Answer Type	Text solution:1
Upvotes	150

In the adjoining figure, show that $A BC D$ is parallelogram. Calculate the area of parallelogram $A BC D$ .

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