Perimeter of a Rectangle
Perimeter of a rectangle is a Grade 4 geometry skill covered in Saxon Math Intermediate 4 Chapter 2. Students apply the formula P equals 2l plus 2w to find the total distance around a rectangle. Because a rectangle has two equal lengths and two equal widths, doubling each and adding the results is a shortcut for adding all four sides. For example, a pool 12 meters long and 5 meters wide has a perimeter of 2 times 12 plus 2 times 5 equals 34 meters. Distinguishing perimeter from area is a key conceptual goal.
Key Concepts
Property For a rectangle with length $l$ and width $w$, the perimeter $P$ can be calculated with the formula: $$P = 2l + 2w$$.
Examples A rectangle with length 8 ft and width 5 ft has a perimeter of $P = 2(8) + 2(5) = 16 + 10 = 26$ ft. A book cover that is 10 inches long and 7 inches wide has a perimeter of $P = 2(10) + 2(7) = 20 + 14 = 34$ inches.
Explanation Since rectangles have two matching lengths and two matching widths, this formula is a cool shortcut! Instead of adding all four sides one by one ($l + w + l + w$), you just double the length, double the width, and add those two results together. It is super efficient!
Common Questions
What is the formula for the perimeter of a rectangle?
P equals 2l plus 2w, where l is the length and w is the width. This doubles each dimension and adds the results.
How do I find the perimeter of a rectangle that is 12 meters long and 5 meters wide?
P equals 2 times 12 plus 2 times 5 equals 24 plus 10 equals 34 meters.
What is the difference between perimeter and area?
Perimeter is the total distance around the outside of a shape and is found by adding sides. Area is the space inside the shape and is found by multiplying length by width.
Can I find perimeter by adding all four sides individually?
Yes. Adding l plus w plus l plus w gives the same result as 2l plus 2w. Both methods are correct.
What happens if I only add one length and one width?
You get only half the perimeter. Always account for all four sides—two lengths and two widths.
Why does the formula P equals 2l plus 2w work?
A rectangle has two pairs of equal sides. Doubling each unique side length accounts for both copies, making the calculation more efficient than listing all four sides.