Question

a field is in the shape of a trapezium whose parellel sides are 25m and 10m. The non- parallel sides are 14m and 13m. Find the area of the field.

Answer 1

Construction- Draw a line BE parallel to AD.
AB=10cm so DE=10cm as it is now a parallelogram.
EC=25-10=15cm.
So perimeter of triangle,
BEC=13+14+15cm=42cm.
s=42/2=21cm.
By Heron's formula,
A=root s×(s-a)(s-b)(s-c)
=root 21×(21-13)(21-14)(21-15)cm2
=root 21×8×7×6cm2
=root 3×7×2×2×2×7×3×2
=7×3×2×2cm2
=84cm2
Area of parallelogram ABED=b×h
=10×13cm2
=130cm2
Area of trapezium field=84+130
=214cm2