parallel sides of a trapezium are 12 and 36 cm respectively.Its non parallel sides are each equal to 15 cm. Find area of trapezium?
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Let ABCD be the trapezium & AB = 36 cm, DC = 12 cm and AD = 12cm.
Now, EB = (AB-AE) = (AB-DC)
= 36 - 12
= 24cm.
In triangle EBC, CE = BC = 15cm.
CF is perpendicular to AB.
F is the midpoint of EB.
EF = 1/2 * AB
= 1/2 * EB
= 1/2 * 24
= 12cm.
In right- angled triangle CFE, CF = 15cm, EF = 12cm.
By Pythagoras theorem, we have
CF = root CE^2 - EF^2
= (15^2 - 12^2)
= root 225 - 144
= root 81
= 9.
The distance between the parallel sides = 9cm.
Therefore, Area of the trapezium = 1/2 * (sum of parallel sides) * (distance)
= 1/2 * (12+36) * 9
= 432/2
= 216 cm^2.
Hope this helps!
Now, EB = (AB-AE) = (AB-DC)
= 36 - 12
= 24cm.
In triangle EBC, CE = BC = 15cm.
CF is perpendicular to AB.
F is the midpoint of EB.
EF = 1/2 * AB
= 1/2 * EB
= 1/2 * 24
= 12cm.
In right- angled triangle CFE, CF = 15cm, EF = 12cm.
By Pythagoras theorem, we have
CF = root CE^2 - EF^2
= (15^2 - 12^2)
= root 225 - 144
= root 81
= 9.
The distance between the parallel sides = 9cm.
Therefore, Area of the trapezium = 1/2 * (sum of parallel sides) * (distance)
= 1/2 * (12+36) * 9
= 432/2
= 216 cm^2.
Hope this helps!
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