Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Area measures the space inside a rectangle and perimeter measures the distance around it. Third graders found both by counting squares and adding sides. In fourth grade, students apply the formulas: area = length × width, and perimeter = 2 × length + 2 × width (or the sum of all four sides). They use them in real-world problems, such as carpeting a room or fencing a garden.
The standard highlights working backward. If a rectangular room has 72 square feet of flooring and is 9 feet long, students view the area formula as a multiplication equation with an unknown factor, 9 × w = 72, and find that the width is 8 feet. Similar thinking finds a missing side from the perimeter. Students should also be able to explain which measurement a situation calls for: fencing is perimeter, tiling is area. Keeping units straight, with feet for perimeter and square feet for area, is part of the work.
Students multiply when a problem asks for fencing, or add sides for carpeting. Ask whether the job covers the inside (area) or goes around the edge (perimeter).
For an 8 by 5 rectangle, students may answer 13 instead of 26. Tracing all four sides with a finger shows each length is used twice.
Writing an area as 40 feet instead of 40 square feet hides the meaning. Area counts squares, so its unit is a square unit.
Given area and one side, some students multiply the two numbers. Writing the formula with a blank, 9 × ___ = 72, shows that division finds the missing side.
A rectangular room needs 72 square feet of flooring. The room is 9 feet long. How wide is it, and what is its perimeter?
Answer: The room is 8 feet wide, and its perimeter is 34 feet.
Grid paper rectangles let students check formulas against counted squares and edges. Ask students to draw two rectangles with the same area but different perimeters (such as 4 by 6 and 3 by 8) to separate the two ideas.
Tests often give one of area or perimeter and ask for the other, which requires finding a missing side first. Practice these two-step problems with clear diagrams.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 84 (also accepted: 84 square cm, 84 cm²)
Area = length × width = 12 × 7 = 84 square centimeters.
Answer: 42 (also accepted: 42 m)
Perimeter = 2 × 15 + 2 × 6 = 30 + 12 = 42 meters.
Answer: 6 (also accepted: 6 feet, 6 ft)
9 × w = 54, so w = 54 ÷ 9 = 6 feet.
Answer: C) Perimeter
A fence goes around the edge of the field, which is the perimeter.
Answer: D) 5 inches
The two lengths use 2 × 10 = 20 inches, leaving 10 inches for the two widths. Each width is 10 ÷ 2 = 5 inches.
Answer: A) 4 by 6 and 3 by 8
4 × 6 = 24 and 3 × 8 = 24, so the areas match. Their perimeters are 20 and 22, which differ.
A full lesson with slides, activities and an exit ticket on area and perimeter of rectangles, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 4.MD.A.3 with an answer key, ready in about a minute.
Make a worksheet →Turn area and perimeter of rectangles into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Area is the number of square units covering a shape. Perimeter is the total length of its edges. Area uses square units; perimeter uses ordinary length units.
Treat the area formula as a multiplication with an unknown factor and divide. If the area is 60 and one side is 5, the other side is 60 ÷ 5 = 12.