6th Grade Math Textbook, Fundamentals

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Graph each polygon. Then find its area. Use each method at least once.

1.A(2, 2), B(4, 7), C(7, 4)

2.A(1, 3), B(5, 7), C(8, 5), D(7, 1)

3.A(2, 2), B(4, 7), C(9, 2), D(5, 3)

4.A(2, 4), B(4, 6), C(6, 4), D(4, 2)

5.A(2, 3), B(3, 9), C(8, 10), D(12, 6), E(8, 5), F(6, 1)

6.Discuss and Write Tell which method you prefer to use and why.

pages 333–334 for exercise sets.

Method 2
Use Pick’s Formula

For this method, each vertex of the polygon must be on a lattice point
(the intersection of two grid lines).

Method 3
Use the Cross Products of the Coordinates

In a table, record the coordinates of the

vertices in clockwise order, starting and

ending with the same point.

Find the cross products of the coordinates

from top left to bottom right, and from

top right to bottom left. The example

shows how to find the first two

cross products.

Add each set of cross products.

Find the difference of the sums of Cross

Products. The area of the polygon is equal

to half of the difference.

Using Pick’s Formula for Hexagon ABCDEF

Number of Boundary Points: 9

Number of Interior Points: 13

A 13  1

16.5 units^2

9

2

  

x

B

CD

E

F

A

7 6 5 4 3 2 1

y

Mark and count all lattice

points on the boundary

(sides) of the polygon.

Be sure to count the

vertices.

Mark and count all

the interior lattice

points (those that are

inside the polygon).

Use Pick’s formula:

AI1, where Iis the

number of interior points and B

is the number of boundary points.

B

2

Cross Products

(right to left)

Coordinates Cross Products

xy(left to right)

43

3 • 7  21 75 4 • 5  20

30 61 7

3 31 6

1 14 12

8 27 7

28 43 6

91 Sums of

Cross Products

58

Difference of the sums  91  58  33

Area of ABCDEF^12 difference 16.5