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In this publication, we will consider various formulas with which you can calculate the height of an isosceles (isosceles) trapezoid.
Recall trapezoid height is called a perpendicular connecting both its bases. Also, the sides are equal.
Finding the height of an isosceles trapezoid
Through the lengths of the sides
Knowing the lengths of all sides of an isosceles trapezoid, you can calculate its height using the formula below:
Through the side and adjacent corner
If you know the length of the side of an isosceles trapezoid and the angle between it and the base of the figure, you can find the height as follows:
Through bases and adjacent angle
You can calculate the height of a trapezoid if you know the lengths of its bases and the angle at any of the bases (for example, at a larger one).
Through area and grounds
Also, the height of an isosceles trapezoid can be found through its area and the lengths of the bases:
This formula can be presented in a different form if instead of the bases the midline is given (m).
m – the middle line, equals half the sum of the bases, i.e. m = (a+b)/2.
Through the diagonals and the angle between them
And one more way to calculate the height of an isosceles trapezoid if you know its diagonals (which have the same length), the angle between them and the bases.
The same formula, but with a middle line (m) instead of the sum of bases:
Note: if the diagonals of an isosceles trapezoid are mutually perpendicular, then its height is equal to half the sum of the bases or, in other words, the midline.
