The parelel side of a trapezium is 65m 40m its nonparallel sides are 39 m56m find the area
make a sketch.
On mine I sketched a rectangle of side 40 and height h, with two right-angled triangles on each end
On the left I had a hypotenuse of 39 , a height of height, and a base of x
On the right , I had a hypotenuse of 56, a height of h and a base of 25-x
so h^2 + x^2 = 39^2 and h^2 + (25-x)^ = 56^2
both can be solved for h^2 and the results equated to get:
39^2 - x^2 = 56^2 - (25-x)^2
solve for x
once you have x, you can find h, the height of the parallelogram (note correct spelling)
area of parallelogram
= (1/2)(h)(40+65)
you do the button pushing
1764
1764m2
To find the area of a trapezium, you can use the formula:
Area = (sum of the parallel sides) * (distance between the parallel sides) / 2
In this case, the parallel sides are given as 65m and 40m, and the distance between the parallel sides can be found by subtracting the shorter non-parallel side from the longer non-parallel side.
Given non-parallel sides:
a = 39m
b = 56m
Now, we can calculate the distance between the parallel sides:
Distance = b - a = 56m - 39m = 17m
Plugging the values into the formula, we have:
Area = (65m + 40m) * 17m / 2
Simplifying the expression, we get:
Area = 105m * 17m / 2
Calculating the area, we have:
Area = 1785m²
Therefore, the area of the trapezium is 1785 square meters.