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.

In triangle ABC, Let, BC = a = 10 cm, AC = b = 16 cm and AB = c = 12 cm. We know that, Semi-perimeter (s) = = = 19 cm. By Heron's formula, We know that, Diagonal of a parallelogram divides it into two triangles of equal area. ∴ Area of triangle ABC = Area of triangle ADC ∴ Area of parallelogram = 2 × Area of triangle ABC. = 2 × 59.9 = 119.8 cm 2 . Let DM be the distance between the shorter sides of the parallelogram. By formula, Area of parallelogram = base × height = BC × DM Substituting the values we get, ⇒ 119.8 = 10 × DM ⇒ DM = ⇒ DM = 11.98 cm. Hence, the distance between shorter sides = 11.98 cm and area of parallelogram = 119.8 cm 2 .

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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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Two adjacent sides of a parallelogram are 15 cm and 10 cm. If the distance between the longer sides is 8 cm, find the area of the parallelogram. Also find the distance between shorter sides.

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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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Mathematics

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.

Mensuration

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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.

Two adjacent sides of a parallelogram are 15 cm and 10 cm. If the distance between the longer sides is 8 cm, find the area of the parallelogram. Also find the distance between shorter sides.

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