Question

The parallel sides of trapezium are 65 and 40 its non parallel sides are 39 metre and 56 metre find the area of the trapezium class 8​

Answer 1

If the height is h, then you have a 40-by-h rectangle in the center, with extra lengths of x and 25-x on the longer base.

$\sf x^2+h^2 = 56^2\\ \sf (25-x)^2+h^2 = 39^2 \\ \sf x^2-56^2 = (25-x)^2 - 39^2\\ \sf x = \dfrac{224}{5}$

$\sf so, h^2 = 56^2-x^2 = \dfrac{28224}{25}\\ \sf h = \dfrac{168}{5}$

$\sf so, the\: area\: is \:=\dfrac{(40+65)}{2} ×\dfrac{168}{5} = 1764$