The parelel side of a trapezium is 65m 40m its nonparallel sides are 39 m56m find the area of trapeyium.
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To find the area of a trapezium, you can use the following formula:
Area = (a + b) * h / 2
where:
- a and b are the lengths of the parallel sides,
- h is the perpendicular distance (height) between the parallel sides.
In this case, the parallel sides are 65m and 40m, and the nonparallel sides are 39m and 56m. We need to find the height of the trapezium.
To find the height, we can use the Pythagorean theorem. In a trapezium, the height forms a right-angle triangle with the nonparallel sides.
Using the Pythagorean theorem, we can calculate the height (h):
h^2 = (b - a)^2 - (c^2 - d^2)
where:
- a = 39m
- b = 56m
- c = ((b - a)/2) = ((56 - 39)/2) = 8.5m (distance from the midpoint of the nonparallel sides to the base)
- d = ((a + b)/2) = ((39 + 56)/2) = 47.5m (distance from the midpoint of the nonparallel sides to the top)
h^2 = (56 - 39)^2 - (47.5^2 - 8.5^2)
h^2 = 17^2 - (2256.25 - 72.25)
h^2 = 289 - (2184 - 72.25)
h^2 = 289 - 2111.75
h^2 = -1822.75
Since the calculated value is negative, it means that there is no real solution for the height. This suggests that the given side lengths do not form a valid trapezium.
Please recheck the values provided, as a trapezium with the given measurements cannot be formed, and therefore, its area cannot be calculated.