Geometry/Trapezoids

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A Trapezoid (American English) or Trapezium (British English) is a quadrilateral that has two parallel sides and two non parallel sides.

Some properties of trapezoids:

The interior angles sum to 360° as in any quadrilateral.
The parallel sides are unequal.
Each of the parallel sides is called a base (b) of the trapezoid. The two angles that join one base are called 'base angles'.
If the two non-parallel sides are equal, the trapezoid is called an isosceles trapezoid.
- In an isosceles trapezoid, each pair of base angles are equal.
- If one pair of base angles of a trapezoid are equal, the trapezoid is isosceles.
A line segment connecting the midpoints of the non-parallel sides is called the median (m) of the trapeziod.
- The median of a trapezoid is equal to one half the sum of the bases (called b₁ and b₂).
A line segment perpendicular to the bases is called an altitude (h) of the trapezoid.

The area (A) of a trapezoid is equal to the product of an altitude and the median.

A=mh

Recall though that the median is half of the sum of the bases.

m={\frac {1}{2}}(b_{1}+b_{2})

Substituting for m, we get:

A={\frac {1}{2}}(b_{1}+b_{2})h

Modern geometry
- Geometry/Algebraic Geometry
- Geometry/Differential Geometry
- Geometry/Algebraic Topology
- Geometry/Noncommutative Geometry

Geometry/An Alternative Way and Alternative Geometric Means of Calculating the Area of a Circle

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