Question

What is the area of a trapezium when height is not given?

Answer 1

a=a+b/2 h is the answer

Answer 2

Trapezium is a bit complicated structure when compared to other four sided figures. But when it is segmented into simpler structures, it would be easier to manipulate to find its area.

Lets segment it into a rectangle, such that the remaining shapes will be two triangles. Finding areas of each shape and adding up will give the total area of the trapezium.

The area of the triangle is calculated using the formula =$\frac{h*b}{2}$. Here, using the Pythogoran theorem the height of the triangle is obtained.

Knowing the height and the length of the rectangle are used to determine the area of the rectangle.

Area of rectangle = length × breadth

Such that, adding all the known areas will give the actual area of trapezium as,

Area of trapezium = Area of triangle 1 + Area of rectangle + Area of triangle 2