The given figure shows parallelograms ABCD and APQR. Show that these parallelograms are equal in area.
Theorems on Area
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Question

The given figure shows parallelograms ABCD and APQR. Show that these parallelograms are equal in area.

KnowledgeBoat · Accepted Answer

We know that, Opposite sides of || gm are equal and parallel. ∴ AB || DC and AR || PQ. We know that, The area of triangle is half that of a parallelogram on the same base and between the same parallels. From figure, || gm ABCD and △ ABR lies on same base AB and between same parallel lines AB and DC. ∴ Area of △ ABR = Area of || gm ABCD ⇒ Area of || gm ABCD = 2 Area of △ ABR .......(1) We know that, Area of triangles on the same base and between the same parallels lines are equal. △ ABR and △ APR lie on same base AR and between same parallel lines AR and PQ. ∴ Area of △ ABR = Area of △ APR ........(2) From equations (1) and (2), we get : ⇒ Area of || gm ABCD = 2 Area of △ APR .........(3) Also, || gm APQR and △ APR lies on same base AR and between same parallel lines AR and PQ. ∴ Area of △ APR = Area of || gm APQR .......(4) Using value of area of △ APR from equation (4) in (3), we get : ⇒ Area of || gm ABCD = Area of || gm APQR ⇒ Area of || gm ABCD = Area of || gm APQR. Hence, proved that the parallelograms ABCD and APQR are equal in area.

Mathematics

The given figure shows parallelograms ABCD and APQR. Show that these parallelograms are equal in area.

Theorems on Area

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Mathematics

The given figure shows parallelograms ABCD and APQR. Show that these parallelograms are equal in area.

Theorems on Area

Related Questions

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area (△ AEC) = area (△ DBF)

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area (△ ABX) = area (quad.ACXD)

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