Drag the slider to move vertex C sideways. The shape completely changes across acute, right, and obtuse triangles, but as long as base AB and height h stay the same, the area never changes.
Ever wonder why the triangle area formula is (base×height)÷2? Draw a parallelogram with the same base and height, and its area turns out to be exactly double the triangle's. That's because flipping a congruent copy of the triangle upside down and attaching it makes exactly a parallelogram.
Why does that work? The triangle area formula is (base × height) ÷ 2. No matter where C sits on the dashed line parallel to the base, its perpendicular distance from base AB (the height) is always the same. Since neither number that goes into the formula (base, height) changes, the area doesn't change either.
Move vertex C with the slider and watch the triangle completely change shape between acute, right, and obtuse — while checking whether the number representing the area stays exactly the same.