M is the midpoint of the side AB of a parallelogram ABCD. If ar(AMCD)=24 cm2, find ar(△ABC).

Question

M is the midpoint of the side AB of a parallelogram ABCD. If ar(AMCD)=24 cm2, find ar(△ABC).

Filo · Accepted Answer

Join the diagonal ACFrom the figure we know that the diagonal AC divides the parallelogram ABCD into two triangles having the same areaIt can be written asArea of △ADC= Area of △ABC......(1)We know that △ADC and parallelogram ABCD are on the same base CD and between the same parallel lines DC and AM.It can be written asArea of △ADC= Area of △ABC=21​ ( Area of parallelogram ABCD)From the figure we know that M is the midpoint of ABSo we getArea of △AMCD= Area of △BMC=21​ ( Area of △ABC)=21​ ( Area of △ADC)It can be written asArea of AMCD= Area of △ADC + Area of △AMCBy substituting the values24= Area of △ADC+21​ ( Area of △ADC)It can be written as 24=23​ ( Area of △ADC)By cross multiplication24×2=3× ( Area of △ADC)On further calculation48=3× ( Area of △ADC)So we getArea of △ADC=348​By divisionArea of △ADC=16 cm2From equation (1)Area of △ADC= Area of △ABC=16 cm2Therefore, Area of △ABC=16 cm2.

Question Text	$M$ is the midpoint of the side $A B$ of a parallelogram $A BC D$ . If $a r (A MC D) = 24 c m^{2}$ , find $a r (△ A BC)$ .
Answer Type	Text solution:1
Upvotes	150

$M$ is the midpoint of the side $A B$ of a parallelogram $A BC D$ . If $a r (A MC D) = 24 c m^{2}$ , find $a r (△ A BC)$ .

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