9.1.1 Developing Formulas for Triangles and Quadrilaterals (continued)
The length of one base of a trapezoid is determined in this example. The lengths of one base, the height, and the area are given. To calculate the length of the other base, substitute the given values into the formula for the area of a trapezoid. Simplify and solve for b 1 . The value of b 1 is found to be 5 inches.
Example 3 Finding Measurements of Rhombuses and Kites
The area of a rhombus or kite with diagonals d 1 and d 2 is A d d . 1 2 = This is the same area as a parallelogram. Imagine taking the rhombus, cutting it along one diagonal and moving the halves to form the parallelogram shown. Now the parallelogram base equals the length of d 2 , and the parallelogram height equals one-half of d 1 . 1 2 The length of one diagonal of a kite is determined in this example. The length of the other diagonal and the area are given. To calculate the length of the diagonal, substitute the given values into the formula for the area of a kite. Simplify and solve for d 2 . The value of d 2 is found to be 11 meters.
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