In the following figure, AC // PS // QR and PQ // DB // SR. Prove that : Area of quadrilateral PQRS = 2 × Area of quad.ABCD.

From figure, PQRS is a parallelogram. Given, AC // PS // QR and PQ // DB // SR. ∴ AQRC and APSC are also parallelograms. We know that, The area of a triangle is half that of a parallelogram on the same base and between the same parallels. From figure, △ ABC and || gm AQRC lie on same base AC and between same parallel lines AC and QR. ∴ Area of △ ABC = Area of || gm AQRC ............(1) △ ADC and || gm ACSP lie on same base AC and between same parallel lines AC and PS. ∴ Area of △ ADC = Area of || gm ACSP ............(2) Adding equations (1) and (2), we get : ⇒ Area of △ ABC + Area of △ ADC = Area of || gm AQRC + Area of || gm ACSP ⇒ Area of quadrilateral ABCD = (Area of || gm AQRC + Area of || gm ACSP) ⇒ Area of quadrilateral ABCD = Area of || PQRS ⇒ Area of || gm PQRS = 2 × Area of quadrilateral ABCD. Hence, proved that area of quadrilateral PQRS = 2 × area of quad. ABCD.

ABCD and BCFE are parallelograms. If area of triangle EBC = 480 cm², AB = 30 cm and BC = 40 cm; Calculate :
(i) area of parallelogram ABCD;
(ii) area of the parallelogram BCFE;
(iii) length of altitude from A on CD;
(iv) area of triangle ECF.

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In the given figure, D is mid-point of side AB of △ ABC and BDEC is a parallelogram.
Prove that :
Area of △ ABC = Area of // gm BDEC.

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ABCD is a trapezium with AB // DC. A line parallel to AC intersects AB at point M and BC at point N. Prove that :
area of △ ADM = area of △ ACN.

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In the given figure, AD // BE // CF. Prove that :
area (△ AEC) = area (△ DBF)

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Mathematics

In the following figure, AC // PS // QR and PQ // DB // SR.
Prove that :
Area of quadrilateral PQRS = 2 × Area of quad.ABCD.

Theorems on Area

Related Questions

ABCD and BCFE are parallelograms. If area of triangle EBC = 480 cm², AB = 30 cm and BC = 40 cm; Calculate :
(i) area of parallelogram ABCD;
(ii) area of the parallelogram BCFE;
(iii) length of altitude from A on CD;
(iv) area of triangle ECF.

In the given figure, D is mid-point of side AB of △ ABC and BDEC is a parallelogram.
Prove that :
Area of △ ABC = Area of // gm BDEC.

ABCD is a trapezium with AB // DC. A line parallel to AC intersects AB at point M and BC at point N. Prove that :
area of △ ADM = area of △ ACN.

In the given figure, AD // BE // CF. Prove that :
area (△ AEC) = area (△ DBF)

Mathematics

In the following figure, AC // PS // QR and PQ // DB // SR.Prove that :Area of quadrilateral PQRS = 2 × Area of quad.ABCD.

Theorems on Area

Related Questions

ABCD and BCFE are parallelograms. If area of triangle EBC = 480 cm2, AB = 30 cm and BC = 40 cm; Calculate :(i) area of parallelogram ABCD;(ii) area of the parallelogram BCFE;(iii) length of altitude from A on CD;(iv) area of triangle ECF.

In the given figure, D is mid-point of side AB of △ ABC and BDEC is a parallelogram.Prove that :Area of △ ABC = Area of // gm BDEC.

ABCD is a trapezium with AB // DC. A line parallel to AC intersects AB at point M and BC at point N. Prove that :area of △ ADM = area of △ ACN.

In the given figure, AD // BE // CF. Prove that :area (△ AEC) = area (△ DBF)

In the following figure, AC // PS // QR and PQ // DB // SR.
Prove that :
Area of quadrilateral PQRS = 2 × Area of quad.ABCD.

ABCD and BCFE are parallelograms. If area of triangle EBC = 480 cm², AB = 30 cm and BC = 40 cm; Calculate :
(i) area of parallelogram ABCD;
(ii) area of the parallelogram BCFE;
(iii) length of altitude from A on CD;
(iv) area of triangle ECF.

In the given figure, D is mid-point of side AB of △ ABC and BDEC is a parallelogram.
Prove that :
Area of △ ABC = Area of // gm BDEC.

ABCD is a trapezium with AB // DC. A line parallel to AC intersects AB at point M and BC at point N. Prove that :
area of △ ADM = area of △ ACN.

In the given figure, AD // BE // CF. Prove that :
area (△ AEC) = area (△ DBF)