Area of a Triangle
Slide the top corner sideways. The triangle leans over, goes long and thin, looks nothing like it did. The area has not moved at all.
Area ½ × 6 × 4 = 12
Slide the top corner — the area stays 12. Only base and height count.
Drag the top corner to move it or change the height, and the end of the base to change the base.
Same base, same height
Ready to try some? Area-of-triangles worksheets
Where it usually goes wrong
The height gets read off the slanted side, because on a leaning triangle that is the side the eye follows. Height is the perpendicular distance from the base up to the top corner — straight up, not along the edge. On a very slanted triangle the leaning side can be twice the height, and the answer comes out twice too big.
Try this
- Slide the top corner sideways as far as it goes. The triangle changes shape completely and the area does not move at all.
- Watch the leaning side get longer while the height stays where it was. Only one of those two numbers is in the formula.
- Press Right, Even and Leaning in turn. Same base, same height, same area, three triangles that look unrelated.
Where this goes next
Half base times height is the piece every other area formula is built from — a parallelogram is two of these triangles, and a trapezoid is two more.
More about area and size
- Circle Circumference and Pithe way around is always 3.14 diameters
- Volume and Surface Area of a Boxvolume and surface area are two measurements that do not keep step
- Scale Factor and Areascaling a figure's sides by k scales its area by k², because area is a product of two lengths and both of them were multiplied by k