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.
First, draw a line segment BE parallel to the line AD. Then, from B, draw a perpendicular on the line segment CD.
Now, it can be seen that the quadrilateral ABED is a parallelogram.
AB = ED = 10 m
AD = BE = 13 m
EC = 25-ED
= 25-10 = 15 m
Now, consider the triangle BEC,
Its semi perimeter (s)
= (13+14+15)/2 = 21 m
By using Heron’s formula,
Area of ΔBEC
= \(\sqrt{s(s - a)(s - b)(s - c)}\)
= \(\sqrt{21(21 - 13)(21 - 14)(21 - 15)}\)m2
= \(\sqrt{21 \times 8 \times 7 \times 6}\)m2
= 84 m2
We also know that the area of ΔBEC = (1/2) × CE × BF
84 cm2 = (1/2) × 15 × BF
BF = (168/15) cm = 11.2 cm
The total area of ABED will be BF × DE
i.e. 11.2 × 10 = 112 m2
∴ Area of the field = 84 + 112
= 196 m2