3.3+Finding+the+Area+of+a+Trapezoid+0809

23/03/09 A.S Big Idea: Equations can be used to Essential Question: What are the distributive and commutative properties useful for? Notes: Three students found out three different methods for finding the area of trapezoids and tested them to see whether they work. We are going to explore the methods and write equivalent expressions for all three methods.
 * How do I complete our wiki assignment?**


 * Problem 3.3**


 * A. Explain each student’s method for finding the area.**

Answer: Tua’s method for finding the area is to divide the trapezoid in half diagonally, creating two triangles. She then multiplied the a by h fro the triangle on the left and divided the product in half. She then multiplied base, b, by height, h, to find the area of the second triangle and divide the product by half. Finally, she added the two products together to find the area of the trapezoid. Sam’s method is to add another trapezoid to the original trapezoid, creating a parallelogram. Then find the area of the parallelogram by multiplying the base by the height and then divide it by half. Carlos’s method for finding the area is to divide the trapezoid in half horizontally and adding another trapezoid, making a parallelogram. He then multiplies h by ½ and multiplies the product by the sum of a plus b.


 * B. Write an algebraic expression to describe each method.**

Answer: For Tua’s method, the algebraic expression would be ½ ah+ ½ bh. For Sam’s and Carlos’s method, the algebraic expression would be ½ h(a+b).

C. Show that the expression you wrote in part B are equivalent.

Answer: The expressions are equivalent because if you substitute 2 for a, 5 for b and 4 for h, the answer to Sam’s and Carlos’s method would be the same, 14. And if you solve Tua’s expression, the answer would be 4+10 which = 14, so all three expressions are equivalent.


 * Problem 3.3 follow-up**

a. Natasha lost her drawing, but she had written this expression for finding the area of a trapezoid.**
 * 1.

1/2h (b-a) + ha Use this expression to decide what Natasha’s drawing might have looked like. Make a drawing, and use it to help explain Natasha’s method for finding the a**rea.

b. Is Natasha’s expression equivalent to the three expressions in part B? Explain.**

Answer: Yes, Natasha’s expression is equivalent to the three expressions in part B because if you do the substitution from problem C, then the solved expression would be ½ 4 (5-2) + 4(2), so 2 times 3 plus 8 equals 6 plus 8 which equals 14, which is the answer to all the other three expressions. So her expression is equivalent to the three expressions in part B.


 * 2. A trapezoid has a height of 10 centimeters and bases of 9 centimeters and 15 centimeters. Find the area of the trapezoid using each of the four expressions.**

Answer: Tua’s method: R=1/2 ah + ½ bh ½ [9(10)] + ½ [15(10)] = ½ (90) + ½ (150) = 45+ 75 = R= 120

Sam’s and Carlos’s method: R= ½ h (a+b) ½ 10 (9+15) = 5(24) = R= 120

Natasha’s expression: R= ½ h (b-a) + ha ½ 10 (15-9) + 10(9) 5(6) +90 30 + 90 R= 120