Math Forum - Problems Library - Middle School, Area

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Middle School: Area

In grades 6-8, students explore the relations among similar objects, solving problems that link length, perimeter, area, and volume. To do so, students learn to calculate the surface area of a variety of objects.

Problems that allow middle-school students to practice finding the area of two- and three-dimensional objects are listed below. They address the NCTM Geometry Standard for Grades 6-8 expectation that students will be able to analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

For background information elsewhere on our site, explore the Middle School Geometry area of the Ask Dr. Math archives. For relevant sites on the Web, browse and search Euclidean Plane Geometry in our Internet Mathematics Library; to find middle-school sites, go to the bottom of the page, set the searcher for middle school (6-8), and press the Search button.


Access to these problems requires a Membership.

The Big Picture! - Judy Ann Brown
Pre-Algebra, difficulty level 3. A picture is enlarged to four times its area. ... more>>

Building Fences - Judy Ann Brown
Pre-Algebra, difficulty level 3. Plan a garden so as to maximize the area surrounded by a 36-yard fence. ... more>>

Building on Water - Judy Ann Brown
Pre-Algebra, difficulty level 4. Find the area of a circular pond not covered by a rectangular building. ... more>>

Chamique the Archer - Mr. Marthinsen's Geometry Class
Pre-Algebra, difficulty level 3. Chamique wants to know the probability of hitting a bull's-eye with a randomly shot arrow. ... more>>

Cubic Changes - Lisa Lavelle
Math Fundamentals, difficulty level 4. Determine how the volume and surface area of a cube change when the edge length is changed. ... more>>

Dividing Daffodils - Suzanne Alejandre
Pre-Algebra, difficulty level 4. Help us plant our garden of daffodils. ... more>>

Exploring Area - Judy Ann Brown
Pre-Algebra, difficulty level 4. Find information about Pick's theorem and solve an area problem using this method. ... more>>

Frugal Flooring - Marita Paynter
Math Fundamentals, difficulty level 2. Help Graeme determine how many tiles he needs to decorate his new bedroom and whether or not he can afford them. ... more>>

Funny Ducks - Ethel Breuche
Algebra, difficulty level 4. These funny ducks always walk exactly three feet from the lily pond. What is the area of the region bounded by their path? ... more>>

Golfing Luck? - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Work with probability on the practice hole of the golf course. ... more>>

The Good Samaritan - Piedmont High School 2nd- and 7th-period Geometry Classes
Pre-Algebra, difficulty level 4. Can the butler afford the paint needed to repair the sign? Did the butler do it? ... more>>

Graphing for Area - Judy Ann Brown
Pre-Algebra, difficulty level 2. Graph six points and find the area of the resulting hexagon. ... more>>

Green Pastures - Carol Dormuth
Trig/Calc, difficulty level 1. Find the area of the cow's grazing pasture. ... more>>

He Ate It All! - Mr. Marthinsen's Geometry Class
Pre-Algebra, difficulty level 3. The professor ate an entire pizza in 28 minutes. Figure out the size of the pizza. ... more>>

How Large is the Patio? - Judy Ann Brown
Middle School, difficulty level 2. The Smiths are putting new flagstone on their patio. How many square feet will the patio cover? ... more>>

How Wide Is My Garden? - Judy Ann Brown
Pre-Algebra, difficulty level 3. A scale drawing is used to determine the width and area of a garden. ... more>>

Lawn-Mowing Chore - Judy Ann Brown
Math Fundamentals, difficulty level 4. Find the area of the yard that Josh, Sam, and Mark must mow. ... more>>

Lost in Space - Lisa Lavelle
Math Fundamentals, difficulty level 4. Figure out how big an error the engineers made when they mixed up their units. ... more>>

The New Rug - Lisa Lavelle
Elementary, difficulty level 3. Find the number of squares needed to cover the Reading area. ... more>>

Office Tile Choice - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the total cost of purchasing tiles for my office. ... more>>

One Area - Many Solutions - Leigh Nataro
Trig/Calc, difficulty level 2. Find the area of a triangle given the coordinates of its vertices. ... more>>

Partial Area - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the area of the portion of the circle that is not included inside the inscribed square. ... more>>

Pi Day - Let's Eat Cake! - Judy Ann Brown
Pre-Algebra, difficulty level 3. In honor of Pi Day we will be comparing the volumes of slices taken from round and rectangular cakes. ... more>>

Pizza Pie - Judy Ann Brown
Pre-Algebra, difficulty level 3. Use the given information to decide how many slices of the small pizza would be equal to or greater than 3 slices from the large pizza. ... more>>

Quilting Squares - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Help with some quick calculations of the amount of fabric needed for this quilt design. ... more>>

Rabbit's Run - Lisa Lavelle
Math Fundamentals, difficulty level 1. Help Regina develop options for building her rabbit's run. ... more>>

Shine On Harvest Moon - Judy Ann Brown
Pre-Algebra, difficulty level 2. Find the area of the largest circle that can be cut from a nine-inch by twelve-inch sheet of paper. ... more>>

Spring Garden Planning - Judy Ann Brown
Pre-Algebra, difficulty level 4. Find the area as well as the length and width of my fractional garden. ... more>>

A Stellar Garden - Bill Marthinsen
Pre-Algebra, difficulty level 3. Martha Stewart wants to rebuild her ugly garden. She needs help calculating the areas in the new garden. ... more>>

A Surfer's Tessellation - Mr. Marthinsen's First Period Class
Pre-Algebra, difficulty level 2. Shane is re-tiling his surf shack. How many of each kind of tile will he need, and what does a big tile cost? ... more>>

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