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TRAPEZOID
DEFINITION
A trapezoid is a quadrilateral that has A PAIR OF OPPOSITE PARALLEL SIDES.
Lines are said to be
PARALLEL if they
are always the same
distance apart and
point in the same
direction so that they
will never meet.
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.
INTERESTING FACTS:
- Like an isosceles triangle that has at least two equal sides, an isosceles trapezoid has equal sides and angles.
- 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 one point perspective of a SQUARE from a bird's eye view or a worm's eye view so that it looks like a box that has been "squeezed" from two corners.
A bird's eye view is an elevated view of an object from above, with a perspective as though the observer were a bird, often used in the making of blueprints, floor plans and maps. It can be an aerial photograph, but also a drawing. (Wikipedia)
CloseA worm's eye view is a view of an object from below, as though the observer were a worm; the opposite of a bird's-eye view. (Wikipedia)
One Point Perspective -
is a drawing method where
parallel lines appear to
converge at one(1) point
ON the HORIZON to give
the illusion of 3D.
If it is an isosceles trapezoid, another helpful way of thinking of this shape is to think of an equilateral triangle and isosceles triangle which looks like a pyramid or volcano with its "top" blown off.
An EQUILATERAL
TRIANGLE is a 2D
shape with ALL
EQUAL SIDES
and ANGLES.
An ISOSCELES
TRIANGLE is a
2D shape with
AT LEAST TWO
EQUAL SIDES.
Average - is the sum of values divided by the total number of values (for example, the average of 6 and 4 is 5; (6+4)/2 = 10/2 = 5)
TRADITIONAL FORMULA
DEFINITIONS:
- 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.
- The 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.
THINKING INSIDE THE BOX METHOD
If you place an ISOSCELES TRAPEZOID inside of a box (a rectangle or a square) and then,
- CUT one side of the trapezoid from the highest point on the trapezoid to form a right triangle
- MOVE the right triangle up and across to the opposite side of the trapezoid, flip it vertically and then move it into place to create a rectangle or a square
If you place a REGULAR TRAPEZOID inside of a box (a rectangle or a square), and then
- CUT both non-parallel sides in the middle to form two small triangles
- FOLD both triangles to the same side of the trapezoid to obtain a rectangle or a square
KEY: Since a trapezoid can be thought of as a rectangle or square that has been "squeezed," instead of having to learn another formula (AreaTrapezoid = median × height), treat the median [(base1 + base2)/2] as the width and use the rectangular formula (height x width) instead. See STEP-BY-STEP SOLUTIONS for detail examples.
STEP-BY-STEP SOLUTIONS
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 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 (AreaTrapezoid = height x width).
AreaTrapezoid = 3 in x 5 in = 15 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. Median (width) = (base1 + base2)/2 = (2.5 in + 5.5 in)/2 = 8 in/2 = 4 in
- Use the rectangle formula instead (AreaTrapezoid = height x width).
AreaTrapezoid = 3 in x 4 in = 12 in2
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.
