Question

The area of a trapezium whose parallel sides are 25 m, 10 m and non-parallel sides are 14 m, 13 m is

• A. $156m^2$
• B. $196m^2$
• C. $218m^2$
• D. $208m^2$

Answer 1

The correct option is B $196m^2$

Let ABCD be a trapezium in which AB = 10 m, BC = 13 m, CD = 25 m and AD = 14 m.
By construction, BE || AD and BF ⊥ CD.


Thus, ABED is a parallelogram.
Let BF = h.
In ΔBEC, BE = 14 m, EC = 15 m, BC = 13 m.
Semi-perimeter,(s)= $\frac{14+15+13}{2}$
= 21 m
Area of $\Delta BEC=\sqrt{21(21-14)(21-13)(21-15)}$ (By Heron's formula)
$\Rightarrow \frac{1}{2}\times EC\times BF=\sqrt{21\times 7\times 8\times 6}$
$\Rightarrow \frac{1}{2}\times 15\times h=\sqrt{7\times 3\times 7\times 4\times 2\times 2\times 3}$
$\Rightarrow \frac{15h}{2}=7\times 3\times 2\times 2$
$\Rightarrow h=\frac{84\times 2}{15}$
$\Rightarrow h=\frac{56}{5}m$
∴ Area of trapezium ABCD = $\frac{1}{2}\times (AB+CD)\times BF$
= $\frac{1}{2}\times (10+25)\times \frac{56}{5}$
= $\frac{1}{2}\times 35\times \frac{56}{5}$
=$7\times 28$
$=196m^2$
Hence, the correct answer is option (b).