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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Question

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.

KnowledgeBoat · Accepted Answer

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 cm². 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 cm². Hence, area of △AOD = 18 cm².

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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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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