Name: ____________________________________ 11-3 NotesGeometry Per _________ Date:______________

Today’s Goal: How do you approximate the area of a curved region?

WARM-UP Investigation 1 1) What is the system of inequalities that results in the shaded region below?

2) What is the area of that region?

Investigation 2*Just Discuss: What are some ways we could wecould calculate area of this irregular figure?

Investigation 3If it takes one can of paint to cover a unit square in the coordinate plane, how many cans of paint are needed to paint the region within the curved figure?

How might we do this? Discuss!

Under approximate: First, since we know how to find the area of a half square region, find how many squares and half squares fit inside the region.

Over approximate: Now consider the area of the region just outside the curve. How many cans of paint does it take if we count the squares and half squares?

Take the ______________ of an ________________________ and an __________________________!

*Suggestion: use colors! *Count FULL/COMPLETE whole and half squares only!

Whole Boxes:

Half boxes:

Area (under approx.):

Whole Boxes:

Half boxes:

Area (over approx.):

1s

2n

3r

Let’s TRY! Many ponds in the Southeast are watershed ponds that have been built by damming valleys. These ponds are usually irregular in shape. If I wanted to know how much area the pond behind my house takes up, what would be the best method to figure this out? Remember, not all county offices keep accurate records on it’s geography, so we’ll come up with the best way to estimate the area ourselves.

Under-estimation: ___________

Over-estimation: ___________

The average area of the pond is: ___________

SUMMARY OF FINDING THE AREA OF A CURVED REGION

1. Count all whole and half squares that fit ___________ the curved region.

2. Count all whole and half squares that make-up the area _______________________________________ of the curve.

3. Take the average of the under-estimation and the over-estimation to get a close __________________ of the curved region.

Whole Boxes:

Half boxes:

Area (under approx.):

Whole Boxes:

Half boxes:

Area (over approx.):

Name: ____________________________________ 11-3 PracticeGeometry Per _________ Date:______________

1. If it takes one can of paint to cover a unit square in the coordinate plane, how many cans of paint are needed to paint the region within the curved figure? Be as precise as possible!

2. What is the closest approximation of the figure below? Show all of your work!

3. What is the closest approximation of the shaded region below? Show all of your work!

4. Given the region shown:

a. Name three points in the region.

b. Identify the coordinates of the four vertices.

c. Write the system of inequalities describing this region.

What is the area of your footprint?

On the graph paper provided to you, trace the outline of your shoe.This outline should result in a curved region.

Under-approximation Over-approximation

Under-estimation: ___________

Over-estimation: ___________

The average area of my shoe is: ___________ boxes.

*If each box is 3x3cm, what is the closest approximation of your footprint? (the area of 1 box is 9cm2)

Whole Boxes:

Half boxes:

Area (under approx.):

Whole Boxes:

Half boxes:

Area (over approx.):

Name: ____________________________________ 11-3 HomeworkGeometry Per _________ Date:______________

* Fill in your road map!!1) What is the approximate area of the figures below? Show all of your work the supports that you have found the closest approximation.

a) Under-approximation

Over-approximation

b)

Whole Boxes:

Half boxes:

Area (over approx.):

Whole Boxes:

Half boxes:

Area (over approx.):

2) Given the quadrilateral with vertices (-10,1), (4, 8), (8, 0), and ( 0,-8), describe this region with a system of inequalities.

Is the point (1,3) in the solution set of the system you wrote above? How do you know?

3) a. Error Analysis! Find the error that the student made and correct it.

y > 32x + 6

y < 23x + 6

y > 0

b. What is the area of the shaded region below?