question_answer

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)  \[\sqrt{3}:1\]              

B)  \[\sqrt{2}:1\]

C)  \[\sqrt{5}:2\]              

D)  \[2:\sqrt{5}\]

Correct Answer: A

Solution :

As shown in figure, ADE is a triangle. \[s=\frac{a+b+c}{2}.\] \[\frac{\sqrt{3}}{2}{{(side)}^{2}}.\] or \[=\sqrt{3}\] By symmetry, FC = 6 cm. Let AB=x Then, \[\Delta ABC=\frac{1}{2}\times base\times height=\frac{1}{2}\times BC\times AD\] or   \[\Delta ABC\] or \[\Delta ABC=\frac{1}{2}\times BC\times AB\]. \[ABCD=AB\times BC=l\times b\] Area of trapezium\[=l+b+l+b\]