Divide Triangle Asymmetrically

Calculator for height and area of an isosceles triangle divided parallel to the base. The division does not take place through the tip, which would result in two equal parts when bisected, but in such a way that another triangle and a quadrangle, namely a isosceles trapezoid are created. Hereby the area of the triangle is smaller than that of the trapezoid for the same height. The relationship between height and area of the new triangle (left part) is quadratic. If the height is half the original one, then the area is one quarter, if height is one third, the area is one ninth, and so on. The angle of the triangle is irrelevant.

Default values are specified for the triangle that is to be divided. These can be changed, please enter two of the three values. The height is the length of the perpendicular from the middle of the base to the opposite vertex. For the length of the legs, i.e. the two sides of equal length of the triangle, further information is required. Calculations with this can be made using the calculator for the isosceles triangle linked above.
With the slider below the triangle you can adjust the size of the parts. Or you can enter a value of the left triangle and press Calculate.
Delete default deletes the values of the entire triangle, Delete parts those of both parts. Bisect calculates the values for half the area.

For example, if the given isosceles triangle with height 10 and base length 3 is halved, the newly created triangle on the left has height 7.07 and base length 2.12. The newly created isosceles trapezoid on the right has the height 4.63, the lower base length of the original triangle, and the upper length is that of the base of the new triangle.