The parallel sides of a trapezium are 48 cm and 20 cm. Its non-parallel sides are 26 cm and 30 cm. What is the area (in cm²) of the trapezium?

Correct option is B

​$$\textbf{Given:} \\\text{Parallel sides of trapezium} = 48 \text{ cm},\; 20 \text{ cm} \\\text{Non-parallel sides} = 26 \text{ cm},\; 30 \text{ cm} \\\textbf{Concept Used:} \\\text{Area of trapezium and Pythagoras theorem} \\\textbf{Formula Used:} \\\text{Area of trapezium} = \frac{1}{2}(a+b)h \\h^2 = \text{(slant side)}^2 - \text{(base part)}^2 \\\textbf{Solution:} \\\text{Difference of parallel sides} = 48 - 20 = 28 \\\text{Let the two parts of base be } x \text{ and } (28 - x) \\\text{Height } = h \\\text{From the side } 26 \text{ cm:} \\h^2 = 26^2 - x^2 \\\text{From the side } 30 \text{ cm:} \\h^2 = 30^2 - (28 - x)^2 \\\text{Equating:} \\26^2 - x^2 = 30^2 - (28 - x)^2 \\676 - x^2 = 900 - (784 - 56x + x^2) \\676 - x^2 = 900 - 784 + 56x - x^2 \\676 = 116 + 56x \\560 = 56x \\x = 10 \\\text{So, } 28 - x = 18 \\h^2 = 26^2 - 10^2 \\h^2 = 676 - 100 \\h^2 = 576 \\h = 24 \\\text{Area of trapezium} \\= \frac{1}{2}(48 + 20)\times 24 \\= \frac{1}{2}\times 68 \times 24 \\= 34 \times 24 \\= 816 \\\textbf{Final Answer:} \\816$$​​