A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.
Solution:
ABCD is a trapezium. Non-parallel sides are 14 m and 13 m. Parallel sides are 25 m and 10 m.
Construction: From point C draw
completing parallelogram AECD. Also, draw
.
Now, we have AE=CD=10 m and AD=CE=14 m because AECD is a parallelogram.
So, BE=AB-AE=25-10=15 m
Semi-perimeter of
m
Using Heron’s formula, Area of
(1)
Area of
BE
m
Area of parallelogram AECD
(2)
Adding (1) and (2), we get
Area of trapezium ABCD=Area of
+Area of parallelogram AECD
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