9.1.1 Developing Formulas for Triangles and Quadrilaterals (continued)
The area of a rhombus is determined in this example. The length of the diagonals are given as algebraic expressions. To calculate the area, substitute the given values into the formula for the area of a rhombus. Simplify the expression for area. The area is also an expression with the unknown x .
The area of a kite is determined in this example. The length of the sides of the kite and the length of one segment of a diagonal are given. Begin by determining the length of d 1 , the shorter diagonal. Use the Pythagorean Theorem to determine the length of one-half of the diagonal, which is one leg of a right triangle. Substitute the known length of the other leg and the length of the hypotenuse into a 2 + b 2 = c 2 . The length of the leg is found to be 21 inches, so the length of d 1 is 42 inches. The 21-inch leg is also a leg in the larger triangle that has the other half of d 2 as a leg. Use the Pythagorean Theorem to calculate the length of that leg and add it to 28 inches to find the length of d 2 . The diagonal d 2 is found to be
72 + 28 = 100 inches. The area of the kite is 1/2( d 1 d 2 ) = 1/2(42)(100) = 2100 in 2 .
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