How to find the height of a trapezoid if its sides are known?

| March 9, 2021 | education

To find the height of the trapezoid, knowing the lengths of the side sides of the trapezoid is not enough, there are an infinite number of trapezoids that have the same side sides, but different heights.

The problem becomes solvable if the lengths of the bases are also known, or one of the angles of the trapezoid.

If the lengths of the bases are known, then a straight line is drawn from one of the vertices belonging to the smaller base of the trapezoid, parallel to the other side of the trapezoid.

In this triangle, the lengths of the two sides are equal to the lengths of the corresponding lateral sides of the trapezoid, and the length of the third side is the difference in the lengths of the bases.

The height of this triangle is also the height of the trapezoid; to find it, the formula for finding the height along the three sides of the triangle is used.

If one of the angles of the trapezoid is known, then if it is an acute angle, the height will be equal to the product of the sine of this angle by the lateral side adjacent to it, if this obtuse angle is adjacent to it acute and then the height through the product of the sine and the lateral side.



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