Half the sum of the parallel sides, times the height between them, that is how you calculate the area of a trapezium.
And that is what we learnt at school (to the tune of pop goes the weasel.)
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Here's some more detail, for those who want it:
For a trapezoid where h is the height (ie: the distance between the two parallel sides), and a & b are the lengths of the two parallel sides:
Area = h (a + b) / 2
Proof:
If you look at a trapezoid sitting on the longer of its two parallel sides, you will see that it's actually a rectangle in the middle, with a right-angled triangle on each side.
The area of the rectangle would be:
h x a (where a is the shorter parallel side)
For the two right-angled triangles, if c and d are the lengths of the perpendicular sides, then the areas are:
(h * c) / 2 and
(h * d) / 2
So, we add the two triangle areas together, and cancel:
(h * c + h * d) / 2
= h (c + d) / 2
This can be substituted for the following, since in a trapezoid a + c + d = b, hence c + d = b - a
h (b - a) /2
So, the total area of the trapezoid is the sum of the two formulas:
h (b - a) / 2 + h * a
(multiply the "h * a" part by 2, and divide be 2 as well, to get a common denominator):
= h (b - a) / 2 + 2ha / 2
= h (b - a + 2a) / 2
= h (b + a) / 2
So, there's your proof. A little complicated, but hopefully you get the idea.
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Area of a square or rectangle: Length x Width Area or a triangle: Base x Hight ÷ 2 Area of a cricle: π x Radius squared Area of a square or rectangle: Length x Width Area or a triangle: Base x Hight ÷ 2 Area of a cricle: π x Radius squared
circle= pi X radius squared
rectangle/square= length X width
parallelogram= base X height
triangle= 1/2 X base X height
Volume = area X height
Half of the base times height.
Area of a circle measured in square units = pi*radius2
Area = length*perpendicular height or 0.5*the product of its diagonals
The formula for calculating the volume of fluid to the fluid container in which it is located. For example. If the container is cylindrical. Area x height = volume of liquid