Question

The perimeter of a trapezium is $52$ cm and its non-parallel sides are each equal to $10$ cm and its altitude is $8$ cm. Its area is

• A. $128c{m}^2$
• B. $112c{m}^2$
• C. $118c{m}^2$
• D. $124c{m}^2$

Answer 1

The correct option is A $128c{m}^2$

As shown in figure, ADE is a triangle. $\therefore D{E}^2={10}^2-8^2=6^2$
or $DE=6cm$
By symmetry, $FC=6$ cm
Let AB =$x$
Then $(x+10+6+x+6+10)=52$
or $2x+32=52orx=10$ cm
$\therefore$ Area of trapezium
Applying the formula for area of trapezium $\frac{1}{2}\times (AB+DC)\times BF$ where $AB$ and $DC$ are parallel sides and $BF$ is distance between them
$=\frac{1}{2}(10+22)\times 8=128c{m}^2$