Triangle Segment

Name: Triangle Segment - Geometry Calculator
Author: Jürgen Kummer

Calculations for a triangle segment. A segment is a strip between two parallel lines. A triangle segment here is defined as one that intersects an isosceles triangle perpendicular to its base such that its vertex lies within the strip, but the two corners between the leg and base are not. This shape is a convex pentagon with two adjacent right angles at the base, two obtuse angles directly above them, and an acute or obtuse angle at the vertex.
Enter the lengths of the base and legs of the original isosceles triangle, as well as the left and right side missing lengths. Choose the number of decimal places, then click Calculate.

Formulas:

c = a - m - n

o = m \cdot b / a \cdot 2

p = n \cdot b / a \cdot 2

f = b - o

g = b - p

d = \sqrt{o^{2} - m^{2}}

e = \sqrt{p^{2} - n^{2}}

h = \sqrt{\frac{4 b^{2} - a^{2}}{4}}

P = c + d + e + f + g

A = \frac{h \cdot a - m \cdot d - n \cdot e}{2}

Lengths, height and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

The height is that of the underlying isosceles triangle. The base length of the pentagon is, of course, the base length of the triangle minus both missing lengths. The length of the missing slopes is the ratio of the leg length to half the triangle base multiplied by the respective missing length. The area is that of the isosceles triangle minus the two right triangles on the left and right.

If the strip does not include the vertex of the isosceles triangle, but is located on one side, then the resulting shape is a right trapezoid. In this case, it doesn't matter whether the underlying triangle is isosceles or not. If the strip is to be cut from a general triangle, then two corresponding right trapezoids can be calculated, in which case the long side of the trapezoids must not be included in the perimeter.

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