QUADRILATERAL

Quadrilateral > Trapezoid

TRAPEZOID

DEFINITION

A trapezoid is a quadrilateral that has A PAIR OF OPPOSITE PARALLEL SIDES.

A drawing showing a regular trapezoid that has two opposite parallell sides and two non-parallel sides.

When the sides that are NOT parallel are equal in length and both angles coming from a parallel side are equal, it is called an Isosceles Trapezoid.

A drawing showing an isosceles trapezoid with sides that are not parallel equal in lenght and both angles coming from a parallel side are equal.

INTERESTING FACTS:

Like a isosceles triangle that has at least two equal sides, an isosceles trapezoid has equal sides and angles. In fact, it is helpful to think of an isosceles trapezoid as an isosceles triangle with its "top" cut off.

A drawing showing anisosceles trapezoid as an isosceles triangle with its "top" cut off.

A trapezoid is called a "trapezium" in the UK but its definition is opposite the US with NO parallel sides.

IT IS HELPFUL TO THINK

It is helpful to think of a TRAPEZOID as looking at a SQUARE from a top-level perspective view.

A drawing showing a trapezoid that looks like a square when viewed from a top-level perspective.

TRADITIONAL FORMULA

FORMULA 1: Area_Trapezoid = (base₁ + base₂)/2 x height

A drawing showing a trapezoid with its base, height and leg measurements.

NOTES:

The BASES are the two (2) parallel sides.
The LEGS are the two (2) non-parallel sides.
The HEIGHT is the distance at right angles from one base to the other base.

FORMULA 2: Area_Trapezoid = median x height

MEDIAN - A trapezoid’s median is the segment that connects the middle of its legs. Its length is equal to the average lengths of the bases (base₁ + base₂)/2.

A drawing showing a trapezoid with its base, height, median and leg measurements.

THINKING INSIDE THE BOX

If you place a ISOSCELES TRAPEZOID inside of a box (a rectangle or a square), then you can MOVE ONE of its side to the opposite side of the trapezoid to obtain a rectangle or a square.

A drawing showign, if you place a ISOSCELES TRAPEZOID inside of a box (a rectangle or a square), then you can MOVE ONE of its side to the opposite side of the trapezoid to obtain a rectangle or a square.

If you place a REGULAR TRAPEZOID inside of a box (a rectangle or a square), then you can FOLD BOTH of its sides to the same sides to obtain a rectangle or a square.

A drawing showing, if you place a REGULAR TRAPEZOID inside of a box (a rectangle or a square), then you can FOLD BOTH of its sides to the same sides to obtain a rectangle or a square.

KEY: As a result, you can use the rectangle formula to determine a trapezoid area where the median is treated as the width.

EXAMPLES

An ISOSCELES trapezoid with a base₁ of 3 in, base₂ of 7 in and a height of 3 in has an area of:

Calculate the median (from Formula 2) which is treated as the width: Median (width) = (base₁+ base₂)/2 = (3 in +7 in)/2 = 10 in/2 = 5 in
Use the rectangle formula instead (Area_Trapezoid = height x width).

Area_Trapezoid = 3 in x 5 in = 15 in²

An ISOCELES trapezoid with a base₁ of 1 in, base₂ of 3 in and a height of 3 in has an area of:

Calculate the median (from Formula 2) which is treated as the width: Median (width) = (base₁+ base₂)/2 = (1 in +3 in)/2 = 4 in/2 = 2 in
Use the rectangle formula instead (Area_Trapezoid = height x width).

Area_Trapezoid = 3 in x 2 in = 6 in²

A REGULAR trapezoid with a base₁ of 2.5 in, base₂ of 5.5 in and a height of 3 in has an area of:

Treat the median as the width (from Formula 2). Median (width) = (base₁+ base₂)/2 = (2.5 in + 5.5 in)/2 = 8 in/2 = 4 in
Use the rectangle formula instead (Area_Trapezoid = height x width).

Area_Trapezoid = 3 in x 4 in = 12 in²

REFERENCE: See screenshots above for graphic representations.

MEMORIZATION TIP

To help remember the different between a trapezoid and a rhombus shape, think of a trapezoid as looking at the back of a car's windshield and think of a rhombus as a slanted box that has been stretched so that all sides are equal.

A drawing showing a trapezoid that looks like a cars' windshield or a square or a rectangle that has been "squeezed" from two corners of two sides equally. Also, a rhombus that looks like a square or a rectangle that has been "pushed" from one corner to caue the shape to "slant" on both sides equally.