ABCD is a parallelogram with side AB = 10 cm. Its diagonals AC and BD are of length 12 cm and 16 cm respectively. Find the area of the parallelogram ABCD.

Let ABCD be a parallelogram with diagonals intersecting at O. Since, diagonals of a parallelogram bisect each other. ∴ AO = = 6 cm and OB = = 8 cm. In triangle AOB, Let AB = a = 10 cm, BO = b = 8 cm and OA = c = 6 cm. We know that, Semi-perimeter (s) = = = 12 cm. By Heron's formula, Since, diagonals of parallelogram intersect each other so O is the mid-point of BD. ∴ AO is the median of the △ABD. Since, median divides the triangle into two triangles of equal area. ∴ Area of △AOB = × Area of △ABD ......(1) Since, diagonal of a parallelogram divides it into two triangles of equal area. ∴ Area of △ABD = × Area of || gm ABCD. Substituting above value of △ABD in equation 1 we get, Area of △AOB = Area of || gm ABCD Substituting values in above equation we get, 24 = Area of || gm ABCD ⇒ Area of || gm ABCD = 24 × 4 = 96 cm 2 . Hence, area of || gm ABCD = 96 cm 2 .

Diagonals AC and BD of a parallelogram ABCD intersect at O. Given that AB = 12 cm and perpendicular distance between AB and DC is 6 cm. Calculate the area of the triangle AOD.

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What is the area of a rhombus whose diagonals are 12 cm and 16 cm?

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ABCD is a parallelogram with sides AB = 12 cm, BC = 10 cm and diagonal AC = 16 cm. Find the area of the parallelogram. Also find the distance between its shorter sides.

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The area of a parallelogram is p cm² and its height is q cm. A second parallelogram has equal area but its base is r cm more than that of the first. Obtain an expression in terms of p, q and r for the height h of the second parallelogram.

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Mathematics

ABCD is a parallelogram with side AB = 10 cm. Its diagonals AC and BD are of length 12 cm and 16 cm respectively. Find the area of the parallelogram ABCD.

Mensuration

Related Questions

Diagonals AC and BD of a parallelogram ABCD intersect at O. Given that AB = 12 cm and perpendicular distance between AB and DC is 6 cm. Calculate the area of the triangle AOD.

What is the area of a rhombus whose diagonals are 12 cm and 16 cm?

ABCD is a parallelogram with sides AB = 12 cm, BC = 10 cm and diagonal AC = 16 cm. Find the area of the parallelogram. Also find the distance between its shorter sides.

The area of a parallelogram is p cm² and its height is q cm. A second parallelogram has equal area but its base is r cm more than that of the first. Obtain an expression in terms of p, q and r for the height h of the second parallelogram.

Mathematics

ABCD is a parallelogram with side AB = 10 cm. Its diagonals AC and BD are of length 12 cm and 16 cm respectively. Find the area of the parallelogram ABCD.

Mensuration

Related Questions

Diagonals AC and BD of a parallelogram ABCD intersect at O. Given that AB = 12 cm and perpendicular distance between AB and DC is 6 cm. Calculate the area of the triangle AOD.

What is the area of a rhombus whose diagonals are 12 cm and 16 cm?

ABCD is a parallelogram with sides AB = 12 cm, BC = 10 cm and diagonal AC = 16 cm. Find the area of the parallelogram. Also find the distance between its shorter sides.

The area of a parallelogram is p cm2 and its height is q cm. A second parallelogram has equal area but its base is r cm more than that of the first. Obtain an expression in terms of p, q and r for the height h of the second parallelogram.

The area of a parallelogram is p cm² and its height is q cm. A second parallelogram has equal area but its base is r cm more than that of the first. Obtain an expression in terms of p, q and r for the height h of the second parallelogram.