Explanation:

Here are the details for calculating the area of the trapezium:

- This trapezium is isosceles because the non-parallel sides are equal (39 cm each).

- We calculate the height using coordinate geometry or the Pythagorean theorem by dropping perpendiculars from the ends of one parallel side to the other.

- The distance between the parallel sides (base) can be seen as the solid base for height calculations.

- By dropping heights, using the properties of an isosceles trapezium, these perpendiculars divide the trapezium into a rectangle and two right-angled triangles.

- The height (h) can be calculated using the Pythagorean theorem where \( h^2 + \left(\frac{51 - 21}{2}\right)^2 = 39^2\).

Calculate:

$$ h^2 + 15^2 = 39^2 $$

$$ h^2 + 225 = 1521 $$

$$ h^2 = 1296 $$

$$ h = 36 \, \text{cm} $$

- Area formula for trapezium: \( \text{Area} = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height} \).

$$ \text{Area} = \frac{1}{2} \times (51 + 21) \times 36 $$

$$ \text{Area} = \frac{1}{2} \times 72 \times 36 $$

$$ \text{Area} = 36 \times 36 = 1296 \, \text{cm}^2 $$

- Correct Answer: Option 2, 1296

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