9.1.1 Developing Formulas for Triangles and Quadrilaterals (continued)
The height of a rectangle is determined in this example. The length of the base (or one side) of the rectangle is given. The area of the rectangle is given as an algebraic expression. Substitute the known values into the formula for area and solve for the unknown h . The height is found to be 2 x + x 3 cm.
The perimeter of a rectangle is determined in this example. The length of the base of the rectangle is given. The area of the rectangle is given as an algebraic expression. Begin by determining the height. The formula for area relates the area to the height and base (or side) length of the rectangle. Substitute the known values into the formula for area and solve for the unknown h .The height is found to be 2 x 2 inches. The formula for the perimeter of a rectangle is P = 2 h + 2 b . Substitute the values for b and h into the formula. Simplifying yields P = 4 x 2 + 34 inches.
Example 2 Finding Measurements in Triangles and Trapezoids
The area of a trapezoid with bases b 1 and b 2 and height h is A b b h ( ) . 1 2 = + This formula is the same as the formula for half the area of a parallelogram formed by two congruent trapezoids. To visualize why this is the case, add an inverted congruent trapezoid to one end of a trapezoid and see what the area of the parallelogram formed would be. 1 2
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