Trapezoid
A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel (marked with arrows below):
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| Trapezoid | Isosceles Trapezoid |
A trapezoid:
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has a pair of parallel sides |
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is an isosceles trapezoid when it has equal angles from a parallel side |
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is called a "trapezium" in the UK (see below) |
Play with a trapezoid:
The parallel sides are the "bases"
The other two sides are the "legs"
The distance (at right angles) from one base to the other is called the "altitude"
Area of a Trapezoid
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The Area is the average of the two base lengths times the altitude: Area = a+b2 × h |
Example: A trapezoid's two bases are 6 m and 4 m, and it is 3 m high. What's its Area?
Area = 6 m + 4 m2 × 3 m = 5 m × 3 m = 15 m2
The Area of Polygon by Drawing tool is helpful when you can draw your Trapezoid.
Median of a Trapezoid
The median (also called a midline or midsegment) is a line segment halfway between the two bases.
The median's length is the average of the two base lengths:
m = a+b2
We can use it to calculate the area:
Area = mh
Do you see how the little triangles flip and move to make that work?
Perimeter of a Trapezoid
The Perimeter is the distance around the edges.
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The Perimeter is the sum of all side lengths: Perimeter = a+b+c+d |
Example: A trapezoid has side lengths of 5 cm, 12 cm, 4 cm and 15 cm, what's its Perimeter?
Perimeter = 5 cm + 12 cm + 4 cm + 15 cm = 36 cm
Trapezium
A trapezium (UK: trapezoid) is a quadrilateral with NO parallel sides.
Watch Out! US vs UK naming
The US and UK have their definitions swapped over, like this:
| Trapezoid | Trapezium | |
|---|---|---|
| US: | a pair of parallel sides | NO parallel sides |
| UK: | NO parallel sides | a pair of parallel sides |