two parallel side AC and DC area of a Trapezium are 12 cm and 36 cm
respectively and non parallel sides are equal to 15 cm find the area of trapezium
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hi , Vikram
We will draw altitudes AF and BE (in green) perpendicuilar to DC.[ fig attached]
Since EF = AB = 12cm, and 12cm is 1/3 of DC which is 36cm
DF amd EC are also12cm each.
We can find altitude AF by applying the Pythagorean theorem to right
triangle ADF:
AF² + DF² = AD²
AF² + 12² = 15²
AF² + 144 = 225
AF² = 81
AF = 9cm
Area of a trapezium = ½ *( sum of the parallel sides )*height,
Area = [AB+DC]/2cm*height,
Area = [12cm+36cm]/2cm*9cm
Area = 48cm/2*9cm
Area = 24cm*9
Area = 216cm² ans
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