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.
Area of a trapezoid = 0.5*(sum of parallel sides)*height
The formula for the area of a trapezoid is A = 1/2 (b1 + b2)/h where b1 is the upper base of the trapezoid , b2 is the lower base of the trapezoid and h is the height of the trapezoid. Since a triangle has only one base , replace either b1 or b2 with zero. Thus the area of a triangle is A = 1/2bh
Area of a trapezoid = 0.5*(sum of parallel sides)*height
from a pyramid
They both use perpendicular height and are in square units. Area of a trapezoid = 0.5*(sum of parallel sides)*perpendicular height Area of a parallelogram = base*perpendicular height
Area of a trapezoid = 0.5*(sum of parallel sides)*height
Area of a trapezoid = 0.5*(sum of parallel sides)*height
Formula for calculating the area of sphere is : 4 * pi * r * r
The formula for the area of a trapezoid is A = 1/2 (b1 + b2)/h where b1 is the upper base of the trapezoid , b2 is the lower base of the trapezoid and h is the height of the trapezoid. Since a triangle has only one base , replace either b1 or b2 with zero. Thus the area of a triangle is A = 1/2bh
Area of a trapezoid = 0.5*(sum of parallel sides)*height
from a pyramid
They both use perpendicular height and are in square units. Area of a trapezoid = 0.5*(sum of parallel sides)*perpendicular height Area of a parallelogram = base*perpendicular height
The formula for calculating the area of a circle is A r2, where A represents the area and r represents the radius of the circle.
Area of a trapezoid: 0.5*(sum of its parallel sides)*height
Yes, a trapezoid can be divided into a rectangle and a triangle, and they can share the same area formula. The area of a trapezoid is calculated using the formula ( A = \frac{1}{2}(b_1 + b_2)h ), where ( b_1 ) and ( b_2 ) are the lengths of the parallel sides and ( h ) is the height. When a trapezoid is divided, the rectangle's area can be calculated using its base and height, while the triangle's area can be calculated using its base and height, which can be combined to match the trapezoid's area formula.
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