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.

Let ABCD be a parallelogram with AC and BD the diagonals intersecting at O. From figure, AB = 12 cm and DM = 6 cm. By formula, Area of parallelogram ABCD = base × height = AB × DM = 12 × 6 = 72 cm 2 . 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 △AOD = × 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 △AOD = Area of || gm ABCD = = 18 cm 2 . Hence, area of △AOD = 18 cm 2 .

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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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.

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Mathematics

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.

Mensuration

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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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Mathematics

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.

Mensuration

Related Questions

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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.