If P is the interoir point of parallelogram ABCD- prove that the sum of area of - PAB and - PDC is as equal to half of the area of parallelogram ABCD -2 MARKS-

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Parallelograms on the Same Base and between the Same Parallels Are Equal in Area

If P is the i...

Question

If P is the interoir point of parallelogram ABCD, prove that the sum of area of ΔPAB and ΔPDC is as equal to half of the area of parallelogram ABCD [2 MARKS]

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Solution

Concept : 1 Mark
Proof : 1 Mark

Draw a line QR parallel to AB and passing through P.

Area of triangle ABP = $\frac{1}{2}$ Area of AQRB

Area of triangle DPC = $\frac{1}{2}$ Area of DQRC

So sum of their areas = $\frac{1}{2}$ Area of AQRB+ $\frac{1}{2}$ Area of DQRC

= $\frac{1}{2}$ Area of parallelogram ABCD

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If P is the interoir point of parallelogram ABCD, prove that the sum of area of ΔPAB and ΔPDC is as equal to half of the area of parallelogram ABCD [2 MARKS]

Concept : 1 Mark Proof : 1 Mark Draw a line QR parallel to AB and passing through P. Area of triangle ABP = 12 Area of AQRB Area of triangle DPC = 12 Area of DQRC So sum of their areas = 12 Area of AQRB+ 12 Area of DQRC = 12 Area of parallelogram ABCD