温馨提示：本站仅提供公开网络链接索引服务，不存储、不篡改任何第三方内容，所有内容版权归原作者所有
AI智能索引来源：http://www.edu.com/math-glossary/Parallelepiped-Definition-Examples
点击访问原文链接

Parallelepiped: Definition and Examples | EDU.COM

进入原网站 导航首页
Parallelepiped: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">ParallelepipedParallelepiped: Definition and ExamplesTable of ContentsParallelepiped: Definition, Properties, and Examples Definition of Parallelepiped

A parallelepiped is a three-dimensional geometric solid with six faces, where each face is a parallelogram. It can also be described as a prism with a parallelogram base. As a polyhedron, it has 666 faces, 121212 edges, and 888 vertices with three pairs of parallel faces joined together. Each face appears to be the mirror image of its opposite face when viewed from outside.

Special cases of parallelepipeds include the cube (with six square faces), the cuboid or rectangular parallelepiped (with six rectangular faces), and the rhombohedron (with six rhombus faces). A parallelepiped's properties include being a solid figure with three dimensions, having three pairs of parallel faces, and featuring face diagonals on each face. Each pair of opposite edges in the same direction has equal length, but edges in different directions may have different lengths.

Examples of Parallelepiped Calculations Example 1: Finding Lateral Surface Area Problem:

Find the parallelepiped's lateral surface area if its base face has opposite sides measuring 555 inches by 777 inches and a height of 666 inches.

Step-by-step solution:

Step 1, Identify the given measurements. We have a=5a = 5a=5 inches and b=7b = 7b=7 inches for the base, and height =6= 6=6 inches.

Step 2, Recall the lateral surface area formula. For a parallelepiped, the formula is:

LSA=2(a+b)×hLSA = 2(a + b) \times hLSA=2(a+b)×h This represents the sum of the areas of the four lateral faces (excluding top and bottom).

Step 3, Substitute the values into the formula.

LSA=2(5+7)×6LSA = 2(5 + 7) \times 6LSA=2(5+7)×6

Step 4, Simplify and calculate.

LSA=2(12)×6=144LSA = 2(12) \times 6 = 144LSA=2(12)×6=144 inches2^{2}2 Example 2: Calculating Painting Cost Problem:

The sides of a parallelepiped's base are given by 777 feet and 111111 feet, respectively. The parallelepiped has a height of 888 feet. Find out how much it would cost to paint its lateral walls for $20\$20$20 per square foot.

Step-by-step solution:

Step 1, Identify the given measurements. We have a=7a = 7a=7 feet, b=11b = 11b=11 feet, and height =8= 8=8 feet.

Step 2, To find the cost, we first need to calculate the lateral surface area using the formula:

LSA=2(a+b)×hLSA = 2(a + b) \times hLSA=2(a+b)×h

Step 3, Substitute the values into the formula.

LSA=2(7+11)×8=2(18)×8=288LSA = 2(7 + 11) \times 8 = 2(18) \times 8 = 288LSA=2(7+11)×8=2(18)×8=288 sq. feet

Step 4, Calculate the total cost by multiplying the lateral surface area by the cost per square foot.

Cost=288×$20=$5,760\text{Cost} = 288 \times \$20 = \$5,760Cost=288×$20=$5,760 Example 3: Finding Total Surface Area Problem:

A rectangular box has dimensions 555 in ×\times× 444 in ×\times× 333 in. Find the total surface area.

Step-by-step solution:

Step 1, Identify the dimensions of the rectangular box. We have length (aaa) = 555 in, width (bbb) = 444 in, and height (hhh) = 3 in.

Step 2, Recall the total surface area formula for a rectangular parallelepiped:

TSA=2(a×b+b×h+h×a)TSA = 2(a \times b + b \times h + h \times a)TSA=2(a×b+b×h+h×a)

Step 3, Substitute the values into the formula.

TSA=2(5×4+4×3+3×5)TSA = 2(5 \times 4 + 4 \times 3 + 3 \times 5)TSA=2(5×4+4×3+3×5)

Step 4, Calculate each part inside the parentheses.

TSA=2(20+12+15)TSA = 2(20 + 12 + 15)TSA=2(20+12+15)

Step 5, Complete the calculation.

TSA=2(47)=94TSA = 2(47) = 94TSA=2(47)=94 in2^{2}2 Comments(2)LLeatherworkerKimNovember 4, 2025I've used this parallelepiped def for my kid's studies. The examples are super helpful, making a tricky topic easy to grasp!

MCMs. CarterSeptember 17, 2025I’ve used the Parallelepiped examples from this page to help my kids visualize geometry concepts better. The painting cost calculation was a fun, practical way to keep them engaged!

Explore More TermsAlgebraKilometerLength ConversionMultiplying FractionsCurved SurfacePartitive DivisionView All Math TermsRecommended Interactive LessonsFind the value of each digit in a four-digit number3Math3.NBT.AUse Arrays to Understand the Associative Property3Math3.OA.B.5Multiply Easily Using the Distributive Property3Math3.OA.B.5Solve the subtraction puzzle with missing digits3Math3.NBT.A.2Word Problems: Addition within 1,0003Math3.NBT.A.2Write Multiplication Equations for Arrays3Math3.OA.A.1View All Interactive LessonsRecommended VideosCount on to Add Within 201Math1.OA.C.5, 1.OA.C.6Count to Add Doubles From 6 to 101Math1.OA.C.5, 1.OA.C.6Multiply by 6 and 73Math3.OA.C.7Understand Division: Number of Equal Groups3Math3.OA.A.2Powers Of 10 And Its Multiplication Patterns5Math5.NBT.A.2Use Models and Rules to Divide Fractions by Fractions Or Whole Numbers6Math6.NS.A.1View All VideosRecommended WorksheetsCombine and Take Apart 2D Shapes1Math1.G.A.2Addition and Subtraction Patterns3Math3.OA.D.9Divide by 6 and 73Math3.OA.C.7Compare Fractions With The Same Denominator3Math3.NF.A.3dUse The Standard Algorithm To Divide Multi-Digit Numbers By One-Digit Numbers4Math4.NBT.B.6Divisibility Rules4Math4.OA.B.4View All WorksheetsRecommended Coloring PagesSimple bridge with a few falling leavesPre-K – KAll SubjectsBlueprint of a crane with bold, clear lines and no backgroundPre-K – KAll SubjectsWaffle with syrup and butter on topPre-K – KAll SubjectsNumber 2 next to a moon with a night sky background1 – 2All SubjectsPumpkin patch with autumn leaves falling and a scarecrow in the background3 – 4All SubjectsButtercup with a detailed background of grass and sky3 – 4All SubjectsView All Coloring PagesRecommended BlogsWhat's a Perfect SAT Score? A Guide for K-6 FamiliesNovember 4, 2025Understanding All Five ACT Sections for K-12 Success: A Guide for Parents, Teachers, and KidsOctober 17, 2025ACT Prep Plan: Creating a Personalized Strategy for High School SuccessOctober 10, 2025ACT vs SAT: Key Differences Parents and Students Should KnowOctober 9, 2025Mastering the ACT: Smart Time Management Tips for Test SuccessOctober 9, 2025Army ASVAB Composite Scores: A Parent's Guide to Military Career PathsOctober 7, 2025View All Blog PostsQUICK LINKSAbout UsPrivacy PolicyTerms of ServiceTOOLSHomework HelperGuide DesignerPodcast MakerPlan BuilderRESOURCESMath GlossaryEnglish GlossaryEnglish Language ArtsMathematicsScienceBook InsightsFun with WordsBlog© 2025 EDU.COM. All rights reserved.

智能索引记录