Bill Zahner Lori Jordan - Saylor Academy
Area and Perimeter ofTrapezoidsBill ZahnerLori JordanSay Thanks to the AuthorsClick http://www.ck12.org/saythanks(No sign in required)
To access a customizable version of this book, as well as otherinteractive content, visit www.ck12.orgCK-12 Foundation is a non-profit organization with a mission toreduce the cost of textbook materials for the K-12 market bothin the U.S. and worldwide. Using an open-content, web-basedcollaborative model termed the FlexBook , CK-12 intends topioneer the generation and distribution of high-quality educationalcontent that will serve both as core text as well as provide anadaptive environment for learning, powered through the FlexBookPlatform .Copyright 2013 CK-12 Foundation, www.ck12.orgThe names “CK-12” and “CK12” and associated logos and theterms “FlexBook ” and “FlexBook Platform ” (collectively“CK-12 Marks”) are trademarks and service marks of CK-12Foundation and are protected by federal, state, and internationallaws.Any form of reproduction of this book in any format or medium,in whole or in sections must include the referral attribution linkhttp://www.ck12.org/saythanks (placed in a visible location) inaddition to the following terms.Except as otherwise noted, all CK-12 Content (including CK-12Curriculum Material) is made available to Users in accordancewith the Creative Commons Attribution-Non-Commercial 3.0Unported (CC BY-NC 3.0) License (http://creativecommons.org/licenses/by-nc/3.0/), as amended and updated by Creative Commons from time to time (the “CC License”), which is incorporatedherein by this reference.Complete terms can be found at http://www.ck12.org/terms.Printed: September 6, 2013AUTHORSBill ZahnerLori Jordan
www.ck12.orgC ONCEPTConcept 1. Area and Perimeter of Trapezoids1Area and Perimeter ofTrapezoidsHere you’ll learn how to calculate the area and perimeter of a trapezoid.What if you were given the dimensions of a trapezoid and asked to calculate its area? How does calculating the areaof a trapezoid relate to calculating the area of a parallelogram? After completing this Concept, you’ll be able toanswer questions like these.Watch ThisMEDIAClick image to the left for more content.CK-12 Foundation: Chapter10AreaandPerimeterofTrapezoidsALearn more aboutthearea oftrapezoids by watching the video atthis link.GuidanceRecall that a trapezoid is a quadrilateral with one pair of parallel sides. The lengths of the parallel sides are the bases.The perpendicular distance between the parallel sides is the height, or altitude, of the trapezoid.To find the area of the trapezoid, let’s turn it into a parallelogram. To do this, make a copy of the trapezoid and thenrotate the copy 180 . Now, this is a parallelogram with height h and base b1 b2 . Let’s find the area of this shape.1
www.ck12.orgA h(b1 b2 )Because the area of this parallelogram is made up of two congruent trapezoids, the area of one trapezoid would beA 12 h(b1 b2 ). The formula for the area of a trapezoid could also be written as the average of the bases time theheight.Example AFind the area of the trapezoid below.1A (11)(14 8)21A (11)(22)2A 121 units2Example BFind the area of the trapezoid below.1A (9)(15 23)21A (9)(38)2A 171 units22
www.ck12.orgConcept 1. Area and Perimeter of TrapezoidsExample CFind the perimeter and area of the trapezoid.Even though we are not told the length of the second base, we can find it using special right triangles. Both trianglesat the ends of this trapezoid are isosceles right triangles, so the hypotenuses are 4 2 and the other legs are of length4. P 8 4 2 16 4 2 P 24 8 2 35.3 units1A (4)(8 16)2A 48 units2Watch this video for help with the Examples above.MEDIAClick image to the left for more content.CK-12 Foundation: rimeter is the distance around a shape. The perimeter of any figure must have a unit of measurement attached toit. If no specific units are given (feet, inches, centimeters, etc), write “units.” Area is the amount of space inside afigure. Area is measured in square units. A trapezoid is a quadrilateral with one pair of parallel sides.Guided PracticeFind the area of the following shapes. Round your answers to the nearest hundredth.1.3
www.ck12.org2.3.AnswersUse the formula for the area of a trapezoid.1. 12 (18)(41 21) 558 units2 .2. 21 (7)(14 8) 77 units2 .3. 21 (5)(16 9) 62.5 units2 .PracticeFind the area and perimeter of the following shapes. Round your answers to the nearest hundredth.1.2.Find the area of the following trapezoids.3.4.5.6.7.8.9.10.Trapezoid with bases 3 in and 7 in and height of 3 in.Trapezoid with bases 6 in and 8 in and height of 5 in.Trapezoid with bases 10 in and 26 in and height of 2 in.Trapezoid with bases 15 in and 12 in and height of 10 in.Trapezoid with bases 4 in and 23 in and height of 21 in.Trapezoid with bases 9 in and 4 in and height of 1 in.Trapezoid with bases 12 in and 8 in and height of 16 in.Trapezoid with bases 26 in and 14 in and height of 19 in.Use the given figures to answer the questions.4
www.ck12.orgConcept 1. Area and Perimeter of Trapezoids11. What is the perimeter of the trapezoid?12. What is the area of the trapezoid?13. What is the perimeter of the trapezoid?14. What is the area of the trapezoid?15. What is the perimeter of the trapezoid?16. What is the area of the trapezoid?5
www.ck12.org17. Use the isosceles trapezoid to show that the area of this trapezoid can also be written as the sum of the area ofthe two triangles and the rectangle in the middle. Write the formula and then reduce it to equal 12 h(b1 b2 ) orh2 (b1 b2 ).18. Quadrilateral ABCD has vertices A( 2, 0), B(0, 2),C(4, 2), and D(0, 2). Show that ABCD is a trapezoid andfind its area. Leave your answer in simplest radical form.6
CK-12 Foundation is a non-profit organization with a mission to reduce the cost of textbook materials for the K-12 market both in the U.S. and worldwide. Using an open-content, web-based collaborative model termed the FlexBook ,
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walkthrough videos accessible through vizHOME. These home visit simulations may also be used with VR Laptop & Oculus Rift equipment. For more information about this simulation resource contact: Susan Zahner . UW-Madison School of Nursing . susan.zahner@wisc.edu. For more information on vizHOME contact: vizHOME@wid.wisc.edu . 1 . Virtual Home Visits . Background: Contemporary trends in health .
Zahner of Biology, and Abraham Axelrud and Jonas Falik of Business (1984-85); and Joanna Ambron and Ernest Zahner of Biology, Abraham Axelrud and Jonas Falik of Business, Pericles Emanuel of ECET, Robert Becker of English, Sandy Siff of Health, Physical Education, and Dance, Sylvia Svitak of
Nathan W. Hartman, Jesse Zahner, Tom Hedberg, Allison Feeney. Title: MINIMUM INFORMATION MODEL Author: Miller, Alexander M Created Date: 4/6/2018 1:38:29 PM .
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