Name: ___________________________

Geometry Period _______

Unit 10: Area

In this unit you must bring the following materials with you to class every day:

Calculator

Pencil

This Booklet

A device

Headphones!

Please note:

You may have random material checks in class

Some days you will have additional handouts to support your understanding of

the learning goals in that lesson. Keep these in a folder and bring to class every

day.

All homework for this unit is in this booklet.

Answer keys will be posted as usual for each daily lesson on our website

Warm-Up (from video notes)

a) 0.025 L into mL b) 45 km into mm

c) 2 m into cm d) 190 mm to cm

Units of measure can be used in the Metric system and the Imperial system

From the Regents formula sheet:

10-1 Conversions Day #2

Conversion acronym!

1-step conversions

a) 5 inches into CM b) 835 inches into meters (nearest 10th)

c) 2 miles into kilometers

2-step conversions

d) 5 miles into inches e) 35800 cm into feet (nearest foot)

Together!

1. A typical marathon is 26.2 miles. Gabby averages 12 kilometers per hour when running in marathons. Determine

how long it would take Gabby to complete a marathon, to the nearest tenth of an hour. Show all work to justify

your answer.

What do we know? What do we need to convert: Solve:

Conversions with COST:

2. Peter is painting a square mural. The length of each side of the mural is 6cm. If the paint costs $0.17 per square inch,

how much will it cost to paint the entire mural?

Your Practice Time!

3. The Utica Boilermaker is a 15-kilometer road race. Marc is signed up to run his race and has done the following runs

to train for the Utica Boilermaker:

I. 10 miles

II. 44,880 feet

Which run(s) are at least 15 kilometers?

1) I, only 2) I and II 3) II, only 4) None of the above

4. Jen is at Harrison Avenue Deli and looking to order sandwich items for her two sons. She wants to buy 8 ounces of

Boar’s Head Turkey. The sign reads “6.95/lb.” How much will she pay for the turkey?

5. Stop and Shop tomatoes cost $1.56 per pound. If Monica purchased 36 ounces of tomatoes, how much did she pay?

Round to the nearest cent.

6. Metric Flashback!

a) 60 kilometers into meters b) 36 km to cm

7. The North building of the Chicago City Center is 1,368 ft tall. Estimate how many yards tall it is.

a) 4560 b) 4104

c) 456 d) 410.4

8. Peter walked 8,900 feet from home to school. How far, to the nearest tenth of a mile, did he walk?

9. A soda container holds 512 gallons of soda. How many pints of soda does this container hold?

10. A parking lot is 100 yards long. What is the length of 3/4 of the parking lot, in feet?

11. Convert the following rate of 75 kilometers per hour to meters per minute?

Preview for tomorrow!

12. Calculate the perimeter of the triangle.

12. Calculate the length of EF, the midsegment of the trapezoid to the nearest 10th of a meter.

Today’s Goal: How do I apply geometry concepts to figure out the area of Triangles and Parallelograms?

1. In your teams, start here: Take out a highlighter and read together as a group

Formulas!

Area of a triangle

Area = 1

2(𝑏𝑎𝑠𝑒)(ℎ𝑒𝑖𝑔ℎ𝑡)

Area of a parallelogram

Area = base length x height

*Remember, rectangles, squares

and rhombuses are parallelograms

so the same rules apply!

Good News!

These are GIVEN to you on

your reference sheet on the

regents:

When solving for area, the unit is

“units squared”

Area is a two-dimensional

concept

2. Note: “HEIGHT” of an object is the distance of the segment that extends from a vertex and is perpendicular to the

opposite side

3. Using the formulas shown above, solve for the area of each of the following:

Triangle Practice Parallelogram Practice

*Note in this example, when you have a right triangle, the

“base” and the “height” is just the legs of the triangle! No

hypotenuse included!

Careful!

Now start making connections. Use each other; there are different cases to consider and information missing!

Using your knowledge of Geometry, you are able to determine the areas of shapes when information is unknown.

10-2 Notes

1. Given the following triangle, answer a- e

a) State the base of the triangle:

b) Label the height of the triangle with an “h”

c) State the height of the triangle: How will you solve for it?

d) Determine the area of the triangle:

2. Given the following triangle, answer a- e

a) State the height of the triangle:

b) State the base of the triangle: How will you solve for it?

Include all 8 decimal values from calculator

c) Determine the area of the triangle to the nearest whole number:

3. Given that BD is a perpendicular bisector, determine the area of triangle ABC.

Show all work to support your answer.

4. Shown below is isosceles triangle MAH. Segment AT is drawn such that it is the angle bisector of <MAH.

Given that m<MAH = 800 and AT is the angle bisector of <MAH, determine and state the area of triangle MAH, round to

the nearest 10th.

Check in with your teacher and then keep going! HW Is to complete

practice!

5. Given rectangle ABCD with diagonal AC, determine and state the area of the following rectangle to the nearest

whole number:

6. Given rectangle ABCD with diagonal BD, determine and state the area and perimeter of the following rectangle:

7. In the following diagram of isosceles triangle ABC, BD is the perpendicular bisector of AC, AC = 6.84 and AB =10.

Determine the length of BD to the nearest 10th.

8. Keep in shape: a) Solve for the side labeled x in the following triangle to the nearest whole number:

b) Using your answer from part a, State the area of the triangle.

9. Determine and state the area of triangle ABC.

10. Given equilateral triangle ABC with angle bisectors drawn in, answer the following parts:

a. Find AP.

b. Find AB correct to four decimal places.

c. Find the area of triangle ABP to the nearest tenth.

d. Optional: Want a challenge? Find the area of triangle ABC to the nearest whole number.

11. The following regular hexagon was divided into congruent triangles. a. Determine the area of triangle ABC

b. Hence, or otherwise, determine the area of the whole hexagon.

12. Determine the area of the following composite figure to the nearest tenth. Show all work to support your answer. Hint: It may help to decompose the shape!

13.

Today’s Goal: How do you calculate the area of a regular polygon?

Gathering Skills for Success!

Fact Check #1: Isosceles Triangles

1) Given the following isosceles triangle with median AD,

We know that AD is also the:

Let’s now mark in what this means!

Fact Check #2: Central Angles

To solve for area in your polygons, you had to find the area of each triangle. We split up polygons into triangles:

*Note these inside triangles whose vertex lie on the center of the polygon are always ______________________. Team Work: The following problems will allow you to solve for the area of a regular polygon today! You will together on these questions in class together. Each problem will require you to use your knowledge of geometry and previously learned content.

Remember: 1) Work together 2) Make sure you re-draw smaller triangles in diagrams 3) Keep Long Decimals in a problem until you are done

4) ROUNDING only happens in your final step! (Even in calculator)!

10-3 Notes

O

2) How can you calculate the measure of <BOC? Try it!

Vocab: This angle is called a central angle! Its angle is on the

center point of the regular polygon.

Begin work here! 1. Given the following isosceles triangle with median AD,

Using skills from your FACT CHECK #1, solve for and label in the diagram:

a) If CB = 10, what is the length of CD?

b) Classify angle ADC:

c) If <BAC = 72o, what is the measure of <CAD?

d) Determine the length of AD to the nearest hundredth (Redraw the mini right triangle)

e) What is the area of triangle BC to the nearest whole number?

2. Consider the following regular pentagon with one isosceles triangle sketched in (triangle AOB)

c. Sketch in the altitude “height” of triangle AOB.

d. Given that <AOB = 72o, and that AB = 8 inches, determine the

height of triangle AOB, show to 5 decimal places.

e. Sketch in the other 4 triangles that fill the pentagon whose vertices all meet at O.

f. Hence, determine the area of the whole pentagon to the nearest square unit.

3. Consider the following regular hexagon. Using strategies that you used above in example 1 and 2, determine the

area of the regular hexagon below to the nearest hundredth.

Need a clue? Start by creating some triangles!

You Try! – Adapt your knowledge!

Complete the following 10-3 Practice for HW!

4. Find the given angle measure for regular hexagon ABCDEF.

a) mCGD b) mCGH

5. A regular octagon whose interior triangle has a height of 10 units.

Find the area of the octagon to the nearest whole number

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

7. Given the following regular octagon, determine its area to the nearest whole number. SHOW ALL

WORK. Go very slow!

Today’s Goal: How do you calculate exact area of composite figures? Let's Review! Fill in the area formulas for each of the following shapes!

Triangle

Parallelogram Trapezoid

Circle

Semi-circle Area =

Area =

Area =

Area =

Area =

1. Conceptual Thinking: How would you calculate the area of the following figure?

Plan It!

Solve It! (to the nearest meter)

10-4 Notes

2. How would you calculate the area of the shaded region in the figure to the right? Plan It!

Solve It!

New Vocabulary Alert! When the directions read, “in terms of Pi,” this means to calculate numbers without Pi and leave Pi in your answer!

Example) Calculate the area of the circle in terms of Pi:

3. Apply it! Calculate the area of the figure below in terms of Pi. *The height of the triangle is 7ft and the diameter of the semi-

circle is 8ft.

Practice

4. A rectangle with dimensions 21.6 x 12 has a right triangle with base 9.6 and a height of 7.2 cut out of the rectangle.

Find the area of the shaded region.

Plan It!

Solve It!

Plan It!

5. Two squares with side length 5 meet at a vertex and together with segment AB form a triangle with base

of 6 units, as shown. Find the area of the shaded region.

Solve It!

Plan It!

6. A designer created the logo shown below. The logo consists of a square and four quarter circles of equal size.

Express in terms of π, the exact area in square inches of the shaded region.

Plan It!

Solve It!

Plan It!

Note, “in terms of Pi” means to

calculate numbers without Pi

and leave Pi in your answer!

10-4 Homework Directions: Complete each of the following problems. Show all work to earn credit.

1) Calculate the area of the figure below:

2) Calcualte the area of the shade region below to the nearest 10th:

3) Determine the area of the shaded region to the nearest tenth

4) Circle and a rectangle (with base 24 cm and height 8 cm). Find shaded area to the nearest square cm)

5) Wood pieces in the following shapes and sizes are nailed together in order to create a sign in the shape of an arrow.

The pieces are nailed together so that the rectangular piece connects to the triangular piece. What is the area of the

region in the shape of the arrow?

Today’s Goal: How do I apply geometry concepts and conversions to calculate costs?

Warm –Up: With your shoulder buddy!

Jose would like to put down new flooring in two sections of his home. He hires a carpenter to measure and install the flooring. The carpenter’s blue prints are seen below. Calculate the total area of these sections. The carpenter is charging Jose $10 per square meter. How much would the flooring cost Jose?

Together! The owner of a golf course needs to re-seed an area of his field shaped like a triangle. He measures the distance shown in the diagram below. Find the total cost of the seeds if the seeds costs $3 for every square yard. Solve it:

10-5 Notes

495 feet

66

0 feet

1. How is this problem different from our WARM UP?

2. What extra step would be necessary here?

Plan it:

Time to play! Solve the following problems in your teams. Check in with key. THE REST WILL BE YOUR HOMEWORK TONIGHT.

PROBLEM 1 The front of a garage needs to be painted. The total area except for the door will be painted. The door is 150 cm high

and 200 cm wide.

A. How many square meters of paint will be needed?

B. If paint costs $1.50 per square meter. Find the total cost of the paint needed to nearest cent.

350 cm

250 cm

120 cm

PROBLEM 2 A walking path at a local park is modeled on the grid below, where the length of each grid square is 10 feet. The town

needs to submit paperwork to pave the walking path.

a) Determine and state, to the nearest square foot, the area of the walking path.

b) Contractors will charge the town $1.5 per square foot. How much will this project cost the town?

PROBLEM 3 Joe needs to replace the carpet in his living room and hallway with

laminate flooring. A floor plan is shown below. He visits Home Depot

and finds out that the laminate he likes is sold for $0.25 per square

inch. How much will Joe need to pay for his new flooring?

Careful! Watch out for units here!

PROBLEM 4 In Mrs. Berg’s backyard there is a garden with a fountain in the center decorated with a right triangular shape. She uses

her measuring tape to measure the sides of the garden and finds that they are 9 yards and 21 yards. She handed the

blueprints to her gardener and asked him to add fresh top soil to the lawn (excluding the fountain). He will charge her

$0.75 per square foot. What will be the total cost of the project?

30°

.5 yr

Note: 1 yard= 3 feet

PROBLEM 5 The school’s athletic director wants to seed the field. The field is shown at right. The landscaper will charge him $10 per

square foot. How much will he need to spend on this project?

Area of Slanted Polygons

Today’s 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?

10-6 Notes

Using the “ Box” Method of calculating area of “ slanted” polygons 1. What’s different here? Calculate the area of the polygon.

Let’s try another Example:

Calculate the area of the polygon shown below.

Notes/Steps for the Box Method

This polygon has “_______ ” sides, or sides that are not to 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”.

Let’s try it!

𝐴1= 𝐴2= 𝐴3= 𝐴4= =

Area of the Box

Beware of the awkward polygon...

What is the mistake???

Let’s try another example:

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?

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

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 = (𝑏1+𝑏2)ℎ

2

Area of a square/ parallelogram/rectangle: ______

B. A = 𝑏ℎ

2

Area of a circle: ______ C. A = 𝑙𝑤 Area of a trapezoid: ______ D. A = 𝜋𝑟2

1.

𝐴1= 𝐴2= 𝐴3= 𝐴4= =

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).

10-6 Homework 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 ∆𝐴𝐵𝐶 ∪ ∆𝐸𝐹𝐷.

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

.