Question

The parallel sides of trapezium are 65 cm and 40 cm. If its non parallel sides are 6 cm and 8cm . Find the area of trapezium.


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Answer 1

Answer:

Distance between the parallel sides squared is a negative number.

This means that this diagram is imaginary, meaning such a trapezium cannot exist in reality.

Step-by-step explanation:

Parallel sides of a trapezium, a = 65 cm, b = 40 cm.

Lets assume, the distance between the parallel sides is h cm.

The non parallel sides are c = 6 cm and d = 8 cm.

Area of the trapezium = Area of rectangle (a x h) - Right triangle having hypotenuse c - Right triangle having hypotenuse d

If the base of Right triangle having hypotenuse c is x,

then, the base of Right triangle having hypotenuse d is a - b -x

$c^2 = x^2 + h^2$

∴ $x^2 = c^2 - h^2 = 36 - h^2$ . . . . . . . . . . equation (i)

$d^2 = (a - b - x)^2 + h^2$

$(a - b - x)^2 = d^2 - h^2$

$=> (25 - x) = \sqrt{d^2 - h^2}$

$=> x = 25 - \sqrt{d^2 - h^2} = 25 - \sqrt{64 - h^2}$

$=> x^{2} = (25 - \sqrt{64 - h^2} )^2 = 625 + 64 - h^2 - 50\sqrt{64 - h^2}$

$36 - h^2 = 689 - h^2 - 50\sqrt{64 - h^2}$ [putting value from equation (i)]

$=> 50\sqrt{64 - h^2} = 689 - 36 = 653$

$=> h^2 = 64 - (\frac{653}{50})^2$ $= (8 + \frac{653}{50} )(8 - \frac{653}{50} )$

∴ Distance between the parallel sides squared is a negative number.

This means that this diagram is imaginary, meaning such a trapezium cannot exist in reality.