Name: ______________________________________10-3 Notes

Geometry Pd. ________Date: _____

10-3 Area of Slanted Polygons

Todays Goal: How do you calculate area of slanted Polygons?

Try Case 1 and Case 2

Case 1. Examine the irregular polygon shown below. Work with your teammates to calculate the area of this polygon. Describe the method will you use.

Case 2. Discuss- can you use the same method with the polygon below? Why/Why not? Give it a shot!

Summarize Thinking

1. What were the differences in the polygons?

2. What made calculating the area of the second polygon more difficult?

Using the Box Method of calculating area of slanted polygons

1. Whats different here? Calculate the area of the polygon.

Notes/Steps for the Box Method

This polygon has _______ sides, or sides that are notto the axes.

Here, we will use the _______ method.

1. Draw the smallest BOX possible that will enclose the shape. Your Box should have sides that are parallel to the x or y axes.

2. This will create smaller polygonal regions outside of the given polygon whose areas are now much easier to calculate! Number each section (including the original polygon) and calculate each individual area (except for the original polygon).

3. Since the whole is equal to the sum of its ____________ All Sub-polygons will add up to the area of the Box.

Lets try it!

=

Lets try another Example:

Calculate the area of the polygon shown below.

Area of the Box

Beware of the awkward polygon...

What is the mistake???

Lets try another example:

Remember!

1. Sketch the Box using a ruler NEATLY.

2. Number Polygons.

3. Subtract the sum of the known polygonal areas from the area of the Box.

*Careful counting when the triangle gets skinny

2. Calculate the area of the polygon shown below.

Think Pair-Share

Discuss

1. What makes a good Box? 2. How does it make our calculations easier?

PRACTICE!!!

Before you begin! Brainstorm with your partners match the following area formulas to the polygon they correspond to.

Area of a triangle: ______

A. A =

Area of a square/

parallelogram/rectangle: ______

B. A =

Area of a circle: ______

C. A =

Area of a trapezoid: ______

D. A =

1.

=

2. Graph quadrilateral MATH with coordinates M(4,-1) A(-4,2) T(-3,4) and H(2,3) . Calculate the area of polygon MATH.

3. Graph and find the area of the quadrilateral with coordinates (1, 3), (2, 8) (3, 9) and (6, 4).

Name: ______________________________________10-3 HW

Geometry Pd. _______Date: _____

Answer the following problems to the best of your ability. Did you fill in your road map yet today??

1. Use the BOX method to find the area of the pentagon with coordinates (2, 2), (5, 7), (8, 3), (9, 0) and (6, 2)

2. Calculate the Area of the polygon shown below.

3. Congruent triangles ABC and EFD overlap to make parallelogram DGCH. Triangle ABC has a height of 7 cm , AC=10 and GI=4. HC is a midsegment of triangle EFD. Calculate the area of .

4. Find the area of the regular polygon to the nearest 10th. Remember to find the apothem first!