Keep the base
The bottom side stays 6 units long as the upper corner moves.
Triangle Shape Lab
Move a triangle vertex to compare side lengths, angle types and area above a fixed base.
Grades 3–5 · Geometry
Your goal
Build an isosceles acute triangle with area 12 square units. The base stays 6 units long.
Reduced motion is on. The controls still update the scene.
This triangle is scalene and obtuse. Its area is 6 square units. The three angles total 180 degrees. One angle is greater than 90 degrees.
The top corner moves on an integer grid above a fixed base. All allowed triangles have positive area. Side classification uses exact squared lengths. Displayed lengths and angles are rounded, so their printed values may add to 179.9 or 180.1 degrees.
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Learn with Triangle Shape Lab
Triangle Shape Lab invites upper elementary students to move one corner above a fixed six unit base. Changing the horizontal position alters the two slanted sides, while changing height also changes area. Students read side lengths, inspect angle measurements and build triangles that meet a side, angle and area goal together. Centered corners reveal isosceles examples, and other positions produce scalene triangles. The controls keep every figure from collapsing, so learners can compare acute, right and obtuse triangles while checking the same base and height relationship.
What to look for
Center the corner
A centered upper corner makes the two slanted sides equal.
Use the height
With this fixed base, each unit of height adds 3 square units of area.
For teachers and curious learners
Connect triangle side and angle classifications with changes in vertex position and height. Ask students to predict what will happen, change one setting, and explain what they observe. Learn gives a starting point. Practice and Challenge offer new goals with the same scene.
The apex uses integer horizontal positions from 0 to 6 and heights from 1 to 6 above a fixed base. Exact squared side lengths determine classifications. Printed lengths and angles are rounded. This grid includes isosceles and scalene triangles, with acute, right and obtuse cases.