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.

Question

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.

KnowledgeBoat · Accepted Answer

(i) 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, △ EBC and || gm ABCD lie on same base BC and between same parallel lines AD and BC. ∴ Area of △ EBC = Area of || gm ABCD ⇒ 480 = Area of || gm ABCD ⇒ Area of || gm ABCD = 2 × 480 = 960 cm². Hence, area of || gm ABCD = 960 cm². (ii) We know that, Parallelograms on equal bases and between the same parallels are equal in area. From figure, Parallelogram ABCD and BCFE lie on same base BC and between same parallel lines AF and BC. ∴ Area of || gm BCFE = Area of || ABCD = 960 cm². Hence, area of || gm BCFE = 960 cm². (iii) 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, △ ACD and || gm ABCD lie on same base AD and between same parallel lines AD and BC. ∴ Area of △ ACD = Area of || gm ABCD ⇒ Area of △ ACD = = 480 cm². Since, opposite sides of parallelogram are equal. ∴ CD = AB = 30 cm. By formula, ⇒ Area of triangle = × base × height ⇒ Area of triangle ACD = ⇒ 480 = ⇒ AP = = 32 cm. Hence, length of altitude from A on CD = 32 cm. (iv) 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, △ EFC and || gm BCFE lie on same base EF and between same parallel lines EF and BC. ∴ Area of △ EFC = Area of || gm BCFE ⇒ Area of △ EFC = = 480 cm². Hence, area of triangle ECF = 480 cm².

Mathematics

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.

Theorems on Area

Related Questions

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.

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

Mathematics

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.

Theorems on Area

Related Questions

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.

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.

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