Q. 144.4( 20 Votes )

A field is

Answer :

Given: Parallel sides of trapezium = 25 m and 10 m

Non – parallel sides of trapezium = =14 m and 13 m


To Find: Area of the field


Concept Used:


If sides of a triangle are a, b, and c, then area of a triangle is given by:



Where s = semiperimeter of the triangle



Diagram:



Construction:


From C, draw CE || DA.


Explanation:


Now, we can see that ADCE is a parallelogram in which AE || CD and AD || CE.


Now, we can get,


AE = 10 m and CE = 13 m


BE = AB – AE [From the figure]


Therefore,


BE = 25 m – 10 m = 15 m


Now Area of trapezium = Area of Parallelogram AECD + Area of triangle ECB


Let us first calculate the area of a triangle,




s = 21 m





Area = 3 × 7 × 4 m2


Area of Δ ECB = 84 m2


We also know that Area of Δ ECB = 1/2 (BE × CL)


84 = 1/2 (15 × CL)


15 × CL = 168


CL


CL = Height of the parallelogram


Now, Area of parallelogram ADCE = Base × Height


Area of parallelogram = 112 m2


Hence, Area of Trapezium ABCD = (84 + 112) m2 = 196 m2.


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