In figure (3) given below, E and F are midpoints of sides AB and CD, respectively, of parallelogram ABCD. If the area of parallelogram ABCD is 36 cm²,
(i) state the area of ∆APD.
(ii) Name the parallelogram whose area is equal to the area of ∆APD.

Question

In figure (3) given below, E and F are midpoints of sides AB and CD, respectively, of parallelogram ABCD. If the area of parallelogram ABCD is 36 cm²,
(i) state the area of ∆APD.
(ii) Name the parallelogram whose area is equal to the area of ∆APD.

KnowledgeBoat · Accepted Answer

Join the diagonals AC and BD as shown below: (i) ∆APD and || gm ABCD are on the same base AD and between the same parallel lines AD and BC. Area of ∆APD = Area of ||gm ABCD = × 36 = 18 cm². Hence, area of ∆APD = 18 cm². (ii) Let diagonals AC and BD meet at point O. In ∆ABC, Since, O is mid-point of AC (as diagonals bisect each other) and E is mid-point of AB so by mid-point theorem, EO || BC ∴ EF || BC. Since, BC || AD so, ⇒ EF || AD. AB || DC (ABCD is a parallelogram) ⇒ AE || DF Since, EF || AD and AE || DF. ∴ AEFD is a parallelogram. EF bisects the parallelogram ABCD in two equal halves as E and F are mid-points of AB and CD and EF || BC || AD. ∴ Area of || gm AEFD = Area of || gm ABCD = × 36 = 18 cm². ∴ Area of ∆APD = Area of || gm AEFD. Hence, AEFD is the required parallelogram which has area equal to the area of ∆APD.

Mathematics

In figure (3) given below, E and F are midpoints of sides AB and CD, respectively, of parallelogram ABCD. If the area of parallelogram ABCD is 36 cm²,
(i) state the area of ∆APD.
(ii) Name the parallelogram whose area is equal to the area of ∆APD.

Theorems on Area

Related Questions

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Mathematics

In figure (3) given below, E and F are midpoints of sides AB and CD, respectively, of parallelogram ABCD. If the area of parallelogram ABCD is 36 cm2,(i) state the area of ∆APD.(ii) Name the parallelogram whose area is equal to the area of ∆APD.

Theorems on Area

Related Questions

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In figure (2) given below, area of ∆ABD is 24 sq. units. If AB = 8 units, find the height of △ABC.

In figure (2) given below, DE is drawn parallel to the diagonal AC of the quadrilateral ABCD to meet BC produced at point E. Prove that area of quad. ABCD = area of ∆ABE.

In figure (3) given below, E and F are midpoints of sides AB and CD, respectively, of parallelogram ABCD. If the area of parallelogram ABCD is 36 cm²,
(i) state the area of ∆APD.
(ii) Name the parallelogram whose area is equal to the area of ∆APD.

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