Question

The area of a trapezium with equal non parallel sides is $168m^2$. If the lengths of the parallel sides are 36 m and 20 m, find the length of the non-parallel sides.

• A. 100 m
• B. 0.1 km
• C. 10 m
• D. 0.001 km

Answer 1

Answer: (C), (D)

The correct options are
C 10 m
D 0.001 km

Suppose ABCD is a trapezium.

Parallel sides are AD = 20 m and BC = 36 m
The area of the trapezium $=168m^2$
According of the trapezium
$=\frac{1}{2}\times (sumofparallelsides\times Height)=168m^2$
$\Rightarrow \frac{1}{2}\times (BC+AD)\times \left(HeightDF\right)=168m^2$
$\Rightarrow \frac{1}{2}\times (36+20)\times DF=168$
$\Rightarrow \frac{1}{2}\times 56\times DF=168$
$\Rightarrow DF=\frac{168}{28}=6m$
Draw a line which is parallel to AB. ABED is a parallelogram.
$AB\parallel ED$ and $AD\parallel BE$
Now, DEF is a right angled triangle.
EF = 8 m
DF = 6 m
$\therefore DE=\sqrt{(EF{)}^2+(DF{)}^2}=\sqrt{64+(6{)}^2}$
$=\sqrt{64+36}$
$=\sqrt{100}=10m$
$\therefore$ The length of the non-parallel side AB = 10 m