Let the bases of the trapezium be a cm and b cm, and the height be h cm.
The formula for the area of a trapezium is given by:
Area of trapezium = 1/2 * (a + b) * h
The formula for the area of a triangle is given by:
Area of triangle = 1/2 * base * height
Given that the area of the trapezium is 3 times the area of the triangle, we have:
1/2 * (a + b) * h = 3 * 1/2 * a * h
(a + b) * h = 3a * h
a*h + b*h = 3a*h
b*h = 2a*h
b = 2a
Since the bases of the trapezium are in a ratio of 2:1, we have:
a:b = 2:1
We know that the perpendicular height of the trapezium is h cm, and the height of the triangle will also be h cm.
Let the base of the triangle be x cm. Therefore, the bases of the trapezium will be 2x cm and x cm.
Using the formula for the area of the trapezium, we have:
1/2 * (2x + x) * h = 3 * 1/2 * x * h
3xh = 3/2xh
Canceling out the common factors, we have:
3 = 3/2
This is not possible, which means there is a contradiction in the given statement.
The area of the trapezium is 3 times the area of the triangle.
The perpendicular height of the trapezium is h cm.
Calculate the value of h.
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