Derive and apply the formula for the area of a trapezoid.

Please follow the steps below and answer the questions as you go along.

Step 1: Fold the rectangle (index card) in half as pictured below

to make a crease. Then unfold the rectangle.

Step 2: Draw two points at the top of the rectangle.

Connect each point to the closest endpoint of the fold

(Not to the bottom of the RECTANGLE)

Step 3: Cut along the two new creases formed (the two small

triangles at the top of the rectangle)

Step 4: Rotate the triangles 180° about the endpoints of the

crease to create a trapezoid. The crease is called the

MEDIAN because it is the line segment joining the

midpoints of the nonparallel sides.

Step 5: Discuss the questions below with your partner. Then answer the questions.

How do the bases of the trapezoid relate to the original rectangle?

How does the area of the rectangle relate to the area of the trapezoid?

How can you find the median of the trapezoid?

Step 6: What do you think is the formula for the area of a trapezoid?

Area of a Trapezoid

10.1– Area of a trapezoid

10.1

Discovery

Day 2

Example 1: Given that the height of a trapezoid is 12.

The bases are 6 and 14. Find:

a) the median b) the area of the trapezoid

Example 2: Given: Trapezoid WXYZ, with height 7, lower base 18, and upper base 12.

Find: The area of WXYZ.

Example 3: Find the shorter base of a trapezoid if the trapezoid’s area is 52, its altitude is 8, and its

longer base is 10.

Example 4: Example 5:

Find the area of the trapezoid below. Find b1 of the trapezoid in which A = 4x2 in

2,

b2 = 3x in., and h = 2x in.

5

5

10

4

W X

Y Z