<meta http-equiv="refresh" content="1; url=/nojavascript/"> Perimeter and Area | CK-12 Foundation
Dismiss
Skip Navigation

3.10: Perimeter and Area

Created by: CK-12

Triangles and Parallelograms

I. Section Objectives

  • Understand the basic concepts of the meaning of area.
  • Use formulas to find the area of specific types of polygons.

II. Cross- curricular-Reflecting Pool dimensions

  • Use the following image from Wikipedia of the Reflecting Pool in Washington, DC.
  • This is Figure 10.01.01
  • www.en.wikipedia.org/wiki/File:Reflecting_pool.jpg
  • Here is the problem.
  • According to Wikipedia, the dimensions of the Reflecting Pool are 2029\;\mathrm{ft} long and 167\;\mathrm{feet} wide.
  • Given this information, what shape is the Reflecting Pool?
  • What is the perimeter of the pool?
  • What is the area of the pool?
  • Draw a diagram to explain your answer.
  • Solution:
  • The shape is a rectangle.
  • The perimeter is 2029 + 2029 + 167 + 167 = 4392\;\mathrm{ft.}
  • The area is 2029 \times 167 = 338,843\;\mathrm{sq. \ ft.}

III. Technology Integration

  • There are two great short videos on this website for area and length.
  • One is an architect and one is on an apartment design.
  • www.thefutureschannel.com/hands-on_math/apartment.php
  • Have students watch the videos.
  • Then you can expand on this by having the students draw a design of their room at home.
  • Students will need to go home and do some measurements and then come back with the area and perimeter of their room.
  • Rooms with unconventional shapes will be the most fun and challenge.
  • Allow time for students to share their work.

IV. Notes on Assessment

  • Assess student work on the Reflecting Pool problem.
  • Is the diagram accurate?
  • Did the students calculate the area correctly?
  • Did the students calculate the perimeter correctly?
  • Provide students with feedback on their work.

Trapezoids, Rhombi and Kites

I. Section Objectives

  • Understand the relationships between the areas of two categories of quadrilaterals: basic quadrilaterals and special quadrilaterals.
  • Derive area formulas for trapezoids, rhombi and kites.
  • Apply the area formula for these special quadrilaterals.

II. Cross- curricular-Room Design

  • Tell students that they are going to design a room that has a trapezoidal shape.
  • Students can complete this in connection with the Technology Integration if you choose.
  • If not, have the students use the dimensions of their own bedroom (they did this in the last lesson), or the classroom or a standard size bedroom (11 \times 10) for example.
  • Students are going to redesign this area as a trapezoid.
  • They want to come as close to the original area as possible.
  • So if the room was 11 \times 10, the area is 110\;\mathrm{sq\ feet.}
  • How can you come close to the same area if the shape of the room is a trapezoid?
  • Students should draw their design on grid paper and explain their thinking.
  • Allow time for students to share their work when finished.

III. Technology Integration

  • This is a website that shows a house designed as a trapezoid.
  • www.momoy.com/2009/04/02/l-house-beautiful-trapezoid-house-design-by-philippe-steubi-architekten-gmbh/
  • Students can look at the trapezoid shape of the house and the floor plan is also included.
  • There are views of the inside of the house and the outside of the house as well as some of the rooms.
  • Conduct a discussion about the house. What would be the challenges of designing and building such a house?

IV. Notes on Assessment

  • Assessment will come with student presentations and work product.
  • What did students learn about the relationship between rectangles and trapezoids?
  • Were they able to come up with a room with an area close to the original?
  • Who got the closest?
  • Provide students with feedback on their work.

Area of Similar Polygons

I. Section Objectives

  • Understand the relationship between the scale factor of similar polygons and their areas.
  • Apply scale factors to solve problems about areas of similar polygons.
  • Use scale models or scale drawings.

II. Cross- curricular-National Mall Mapping

  • Ask students to use the Wikipedia image of the National Mall to create a map of it.
  • This is Figure 10.03.01
  • www.en.wikipedia.org/wiki/National_Mall
  • Then tell the students that the mall is 1.9\;\mathrm{miles} \times 1.2\;\mathrm{miles.}
  • They are going to use what they have learned about scale and measurement to create their own map of the mall.
  • They need to choose a scale to work with.
  • Then they use grid paper to design the mall.
  • When students have the area of the mall correct, they can draw in as many different museums and monuments as they can.
  • Extra details add extra credit to their work.
  • When finished, allow time for students to share their work.

III. Technology Integration

  • Use the following website on the National Mall in Washington DC.
  • www.en.wikipedia.org/wiki/National_Mall
  • Have students complete some research about the mall.
  • Possible questions include:
  • Who designed it?
  • When was it built?
  • What is at the North end?
  • What is at the South end?
  • How many different museums can you visit there?
  • Have you been to the mall?
  • Which museum would you most like to visit or did you enjoy and why?

IV. Notes on Assessment

  • Assess each student map.
  • Is the use of scale done correctly?
  • Are the measurements correct?
  • Is the map accurate?
  • Has the student take the time to add in details?
  • Provide students with feedback on their work.

Circumference and Arc Length

I. Section Objectives

  • Understand the basic idea of a limit.
  • Calculate the circumference of a circle.
  • Calculate the length of an arc of a circle.

II. Cross- curricular-The Pantheon

  • Have students use the image of the floor plan of the rotunda of the Pantheon to calculate the circumference of it.
  • This is Figure 10.04.01
  • www.en.wikipedia.org/wiki/Pantheon,_Rome
  • The diameter of the dome is 142\;\mathrm{ft.}
  • Given this measurement, what is the circumference?
  • Have the students draw a diagram to explain their work.
  • Allow time for students to share their diagrams in small groups.

III. Technology Integration

  • Have students use the following Wikipedia site to research information on the Pantheon.
  • www.en.wikipedia.org/wiki/Pantheon,_Rome
  • Students can use this information to write a short essay.
  • Students should hunt for mathematical information about the Pantheon for their essay.
  • For example, height of the columns.
  • What is a portico?
  • What is a rotunda?
  • Have the students complete this work and then collect it for your review.
  • Extension on initial exercise- have students research the dimensions of the rectangle that connect the portico and the rotunda.
  • What is the area of the rectangle?
  • What is the perimeter?

IV. Notes on Assessment

  • Look at student work.
  • Is it accurate?
  • Does the diagram represent student work?
  • Provide students with feedback on their work.

Circles and Sectors

I. Section Objectives

  • Calculate the area of a circle.
  • Calculate the area of a sector.
  • Expand understanding of the limit concept.

II. Cross- curricular-History

  • Use the following image from the round table used by King Arthur.
  • This is Figure 10.05.01
  • www.crystalinks.com/roundtable.gif
  • The diameter of the round table was 18\;\mathrm{feet.}
  • Given this measurement, calculate the area of the round table.
  • If the table was divided between each of the knights evenly, what is the area of one of the sectors?
  • Draw a diagram to explain your work.
  • Allow students time to share their diagrams when finished.

III. Technology Integration

  • Have students use the following website as a tutorial on area and circumference of circles.
  • www.mathgoodies.com/lessons/vol2/circle_area.html
  • Students can review already learned material.
  • There is also a worksheet section for them to work with and practice solving problems.

IV. Notes on Assessment

  • Examine student diagrams.
  • Were they able to find the correct area of the table?
  • How about the sectors?
  • Does the diagram accurately show their work?
  • Is there anything missing?
  • Provide students with feedback/correction on their work.

Regular Polygons

I. Section Objectives

  • Recognize and use the terms involved in developing formulas for regular polygons.
  • Calculate the area and perimeter of a regular polygon.
  • Relate area and perimeter formulas for regular polygons to the limit process in prior lessons.

II. Cross- curricular-Architecture

  • Use the following image of a roof in the shape of a hexagon.
  • This is Figure 10.06.01
  • www.space-frames.com/commercial buildings/xha28.htm
  • Have the students use the dimensions of this design to figure out the area of the roof of this hexagon.
  • Then have the students draw a diagram and explain how they figured out the area of the hexagon.
  • Allow time for students to share their work when finished.

III. Technology Integration

  • Have students complete some research on where to find hexagons and pentagons.
  • Students can search architecture, nature or their own subject.
  • Ask the students to keep track of the websites that they visit.
  • Students should prepare a presentation of at least five examples of pentagons or hexagons in their given subject area.
  • Students should include diagrams or images with their work.

IV. Notes on Assessment

  • Assess student diagrams.
  • How did the students figure out the area of the roof?
  • Does their method make sense?
  • Did they divide it into triangles?
  • Did they divide it into trapezoids?
  • Provide students with feedback on their work.

Geometric Probability

I. Section Objectives

  • Identify favorable outcomes and total outcomes.
  • Express geometric situations in probability terms.
  • Interpret probabilities in terms of lengths and areas.

II. Cross- curricular-Target Practice

  • Use the following image of a dartboard.
  • This is Figure 10.07.01.
  • www.home.wlu.edu/~mcraea/GeometricProbabilityFolder/Introduction/Problem0/images/images/dartboard.gif
  • Here is the problem.
  • What is the geometric probability of hitting the center of the internal square of the dartboard?
  • Use probability to figure this out.
  • Show your work with a diagram and be prepared to explain your answer.
  • Allow time for students to share their work when finished.

III. Technology Integration

  • Visit the same website that the image came from and explore the solution to the problem.
  • www.home.wlu.edu/~mcraea/GeometricProbabilityFolder/Introduction/Problem0/images/images/dartboard.gif
  • The answer to the problem that the student solved above is there.
  • Have students use this to correct their own work.
  • Show any changes/corrections that they completed.
  • Then explore the other problems on the site.

IV. Notes on Assessment

  • Because students are going to correct their own work during the technology integration, use this as a time to assess student work through observation.
  • Are the students able to apply the concepts of probability to geometry?
  • Refer students back to the text if they are having difficulty.

Image Attributions

Description

Authors:

Grades:

Date Created:

Feb 22, 2012

Last Modified:

Apr 29, 2014
You can only attach files to None which belong to you
If you would like to associate files with this None, please make a copy first.

Reviews

Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
CK.MAT.ENG.TE.1.Geometry.3.10

Original text