Midsegment of a Triangle Calculator
Enter the three side lengths of any triangle to find all three midsegments, the medial triangle perimeter, and both the original and medial triangle areas — all from the Midsegment Theorem.
Half the length of side a
- 1
Side a
a = 8 = 8 - 2
Midsegment parallel to a = a ÷ 2
8 ÷ 2 = 4By the Midsegment Theorem, each midsegment equals half the length of the side it is parallel to.
How does this calculator work?
Each midsegment of a triangle equals half the length of the side it is parallel to (Midsegment Theorem). A 6-8-10 triangle has midsegments of 3, 4 and 5. The three midsegments form the medial triangle, which is similar to the original with one-quarter of its area.
Formula
How this is calculated
A midsegment (also called a midline) of a triangle is a line segment that connects the midpoints of two sides. By the Midsegment Theorem (also called the Triangle Midpoint Theorem), every such segment is parallel to the third side and exactly half its length. Since a triangle has three sides, it has three midsegments, each half the length of its corresponding parallel side.
The three midsegments together form the medial triangle, which is similar to the original triangle with a scale factor of 1/2. Because area scales as the square of the linear dimension, the medial triangle has area equal to (1/2)² = 1/4 of the original triangle's area. The original triangle's area is computed here via Heron's formula: Area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2 is the semi-perimeter.
This calculator validates the triangle inequality (the sum of any two sides must exceed the third side) before computing results — inputs that do not form a valid triangle return a warning. All results assume Euclidean (flat) geometry.
Frequently asked questions
The Midsegment Theorem states that the segment connecting the midpoints of any two sides of a triangle is parallel to the third side and is exactly half its length. Every triangle has three midsegments, one for each pair of sides.
Together the three midsegments form a smaller triangle — the medial triangle — that is similar to the original with sides half as long and area one-quarter as large. The medial triangle also divides the original into four congruent smaller triangles.
Yes — but you need all three sides to validate the triangle and compute its area. If you only need one midsegment, simply divide the length of the side that midsegment is parallel to by 2. No other information is required for that single result.
Also known as
TG we-Calculate Editorial Team. (2026). Midsegment of a Triangle Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/midsegment-of-a-triangle-calculator
TG we-Calculate Editorial Team. "Midsegment of a Triangle Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/midsegment-of-a-triangle-calculator.
TG we-Calculate Editorial Team, "Midsegment of a Triangle Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/midsegment-of-a-triangle-calculator
@misc{wecalculate_midsegment_of_a_triangle_calculator, title = {Midsegment of a Triangle Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/midsegment-of-a-triangle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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