The lengths of the parallel sides of a trapezium are 51 cm and 21 cm, and each of the other two sides is 39 cm.
What is the area (in cm²) of the trapezium?

Correct option is D

Given :

Parallel sides a = 51 cm, b = 21 cm

Non-parallel sides = 39 cm each

Formula Used :

Area of trapezium
​$$\text{Area} = \frac{1}{2}(a+b) \times h$$​​

Solution :

Difference of parallel sides
51 - 21 = 30

Since the non-parallel sides are equal, the trapezium is isosceles.
So each side projects:
​$$\frac{30}{2}$$​= 15

Using Pythagoras theorem to find height ( h ):

$$h = \sqrt{39^2 - 15^2} \\ \ \\= \sqrt{1521 - 225} \\ \ \\= \sqrt{1296} = 36 \\ \ \\\text{Area} = \frac{1}{2}(51+21) \times 36 \\ \ \\= \frac{1}{2} \times 72 \times 36 \\ \ \\= 36 \times 36 = 1296$$​