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The Properties of a Trapezoid

Definitions and formulas for the perimeter of a trapezoid, the area of a trapezoid, properties of the sides and angles of a trapezoid, properties of the sides and angles of an isosceles trapezoid
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perimeter of a trapezoid area of a trapezoid sides and angles
of a trapezoid
properties of the
isosceles trapezoid
   

 

The perimeter of a trapezoid:

trapezoid

To find the perimeter of a trapezoid, just add up all the lengths of the sides:

Perimeter = a + b + c + B

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The area of a trapezoid:

trapezoid

To find the area of a trapezoid...  The longer base (the bottom) is big B and the smaller base (the top) is little b...

Yeah, that's the formula...  But let's check out where it comes from!

Take two copies of the trapezoid (one blue trapezoid and one green trapezoid)... Tip one upside down and stick them together...  Now, you've got a parallelogram. 

Area of a parallelogram base x height 
                                    = ( B + b ) x h

But, this is double of what we need...  So, multiply by 1/2!

two trapezoids stuck together

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The sides and angles of a trapezoid:

trapezoid



The bases (top and bottom) of a trapezoid are parallel.

That's it.  No sides need to be congruent and no angles need to be congruent.  Nothing special happens with the diagonals.

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A special trapezoid is the isosceles trapezoid (like an isosceles triangle)...
Properties of the sides of an isosceles trapezoid:

trapezoid

The bases (top and bottom) of an isosceles trapezoid are parallel.

Opposite sides of an isosceles trapezoid are the same length (congruent).

The angles on either side of the bases are the same size/measure (congruent).

The diagonals (not show here) are congruent.

trapezoid

Adjacent angles (next to each other) along the sides are supplementary.  This means that their measures add up to 180 degrees.

x degrees + y degrees = 180 degrees