Question

Construct a trapezium having parallel sides $25$ cm and $13$ cm; its nonparallel sides are equal, each being $10$ cm. Find the area of the trapezium (in sq. cm).

• A. $148$
• B. $152$
• C. $158$
• D. None of these

Answer 1

The correct option is B $152$

Since non parallel sides of trapezium are equal. So ABCD is a isosceles trapezium.

So, DX becomes equal to YC.

So, DX = YC = (25-13)/2

DX = YC = 6

Now, applying pythagoras theorem in triangle ADX

${AD}^2={DX}^2+{AX}^2{10}^2=6^2+{AX}^{2}AX=8$

Now, area of trapezium ABCD

$=\frac{1}{2}\times (AB+CD)\times AX=\frac{1}{2}\times (25+13)\times 8=152$

So, correct answer is option B.