Area of a Triangle

Draw a rectangle 8 units wide and 5 units high, and cut it along a diagonal: you get two identical triangles. Each triangle is half of the rectangle, so its area is (1/2) × 8 × 5, which is 20 square units.

That gives the rule: the area of a triangle is half of its base times its height. The base is the side it stands on. The height is the straight-up distance from the base to the opposite corner, measured at a right angle to the base, not along a slanted side.

Why half? Every triangle covers exactly half as much as a rectangle with the same base and height, even when the triangle leans: sliding the top corner sideways keeps the base and the height, so the area stays the same. The base times the height gives the rectangle, and the half gives the triangle.