Areas of Quadrilaterals

Objectives:

• Find the areas of squares, rectangles, parallelograms

• Find the areas of trapezoids

Rectangle/Square

• Area of a rectangle or a square is

• base times height h

b

A = bh

Parallelogram

The area of a parallelogram is the product of a base and height.

Why is this the same formula as finding the area of a rectangle?

A = bh

h

b

Justification

• You can justify the area formulas for parallelograms as follows.

• The area of a parallelogram is the area of a rectangle with the same base and height.

Areas of Trapezoids

The area of a trapezoid is one half the product of the height and the sum of the bases.

A = ½ h(b1 + b2)

This is the same as:

A = h(base 1 + base 2)

2

b1

b2

h

Ex. 4: Finding the Area of a Trapezoid

Substitute 4 for h, 3 for b1, and 7 for b2 to find the area of the trapezoid.

A = ½ h(b1 + b2) Formula for area of a trapezoid.

A = ½ (4)(3 + 7 ) Substitute

A = ½ (40) Simplify

A = 20 Simplify

The area of trapezoid WXYZ is 20 square units

8

6

4

2

5 10 15

W(8, 1)X(1, 1)

Z(5, 5)Y(2, 5)

Practice Worksheet

• Work on a few as a class, then work with your group to find the rest of the answers. When your group is finished, get your worksheet corrected by the teacher. Fix any incorrect answers. When it’s all completed, you can get a chrome book and work on the “Quadrilateral Practice Activities” from www.stanochmath.com