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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Answer
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 cm2.
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 cm2.
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