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Trapezoid Activities

Trapezoids are quadrilaterals, or four-sided geometric figures. The defining characteristic of trapezoids is the presence of two parallel sides, called bases, at the top and bottom of the figure. The bases are often referred to with the variables "b" (for the smaller, upper base) and "B" (for the larger, lower base). There are no rules to the relationships between the values of the sides or angles.

Find the Perimeter
- Find the perimeter, or the total measurement around the shape, of a trapezoid by adding the values of all the sides. For a trapezoid with bases of 3 and 6 and sides of 2 and 1, the perimeter would be 3 + 6 + 2 + 1 = 12.
Find the Area
- The area of a trapezoid is defined by the formula (1/2)h * (B + b) where the "h" is the height, or the distance from the lower base to the upper base. The definition comes from the area of a parallelogram, h(B + b). Two trapezoids turned to fit together form one parallelogram, thus the inclusion of the (1/2). For example, in a trapezoid with the bases of 8 and 12 and a height of 6, (1/2)(6) * (8 + 12) = 3 * (20) = 60.
Find the Midsegment
- The midsegment of a trapezoid is a horizontal line that could be drawn through the center of the shape. The midsegment is represented by the formula (b + B) / 2. For example, in a trapezoid with bases of 16 and 10, the midsegment would be (10 + 16) / 2 = 26 / 2 = 13.
Solve Isosceles Trapezoids
- Unlike regular trapezoids, isosceles trapezoids do have rules that apply to the sizes of sides and angles. In these trapezoids, the two non-base sides are the same length. The two angles closest to base "b" are equal to each other. The two angles closest to base "B" are equal to each other. That means that two angles across from each other vertically are supplementary, meaning they add up to 180. This can be used to solve for unknown angles.
  
  For example, in a trapezoid that has an angle of 80 degrees in the upper left corner near base "b", what is the measurement of the angle in the lower left corner by base "B"? Subtract: 180 - 80 = 100 degrees.

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