This page describes how to derive the forumula for the area of a trapezoid by creating a parallelogram from two congruent trapezoids. The formula is simply one half the area of this parallelogram.

- Start with a trapezoid with known base lengths (b1, b2) and altitude (height).
- Make a copy of it.
- Rotate the copy 180°.
- Translate (move) the copy to touch the original.

Click on the "Run" button below to see this in action.

When the two trapezoids are combined in this way, the result is a parallelogram, which has two pairs of opposite, congruent sides.

Recall that the
area of a parallelogram
is its altitude (h) times the length of either base.
From the figure above we see that both base lengths are equal to b1+b2.
So the area of the parallelogram is
Since this is the area of **two** trapezoids we have to divide this by two, giving

This can be rearranged into more familar forms: or

- Polygon general definition
- Quadrilateral
- Regular polygon
- Irregular polygon
- Convex polygons
- Concave polygons
- Polygon diagonals
- Polygon triangles
- Apothem of a regular polygon
- Polygon center
- Radius of a regular polygon
- Incircle of a regular polygon
- Incenter of a regular polygon
- Circumcircle of a polygon
- Parallelogram inscribed in a quadrilateral

- Square
- Diagonals of a square
- Rectangle
- Diagonals of a rectangle
- Golden rectangle
- Parallelogram
- Rhombus
- Trapezoid
- Trapezoid median
- Kite
- Inscribed (cyclic) quadrilateral

- Regular polygon area
- Irregular polygon area
- Rhombus area
- Kite area
- Rectangle area
- Area of a square
- Trapezoid area
- Parallelogram area

- Perimeter of a polygon (regular and irregular)
- Perimeter of a triangle
- Perimeter of a rectangle
- Perimeter of a square
- Perimeter of a parallelogram
- Perimeter of a rhombus
- Perimeter of a trapezoid
- Perimeter of a kite

- Exterior angles of a polygon
- Interior angles of a polygon
- Relationship of interior/exterior angles
- Polygon central angle

- Tetragon, 4 sides
- Pentagon, 5 sides
- Hexagon, 6 sides
- Heptagon, 7 sides
- Octagon, 8 sides
- Nonagon Enneagon, 9 sides
- Decagon, 10 sides
- Undecagon, 11 sides
- Dodecagon, 12 sides

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