Perimeter of a Parallelogram
Perimeter of a Parallelogram is a Grade 8 math skill in Saxon Math Course 3, Chapter 6, where students calculate the total distance around a parallelogram using the formula P = 2(a + b), where a and b are the two distinct side lengths. Since opposite sides of a parallelogram are equal, you only need to know two sides to find the perimeter.
Key Concepts
Property The perimeter of a parallelogram is the total length of its four sides. For a parallelogram with adjacent side lengths of $a$ and $b$, the formula is $P = 2a + 2b$.
Examples A parallelogram with side lengths of 8 cm and 6 cm has a perimeter of $P = 8 \operatorname{cm} + 6 \operatorname{cm} + 8 \operatorname{cm} + 6 \operatorname{cm} = 28 \operatorname{cm}$. For a rhombus where all four sides are 5 meters long, the perimeter is simply $P = 4 \cdot 5 \operatorname{m} = 20 \operatorname{m}$.
Explanation Perimeter is all about the distance around the outside, like building a fence. You simply add up the lengths of all four sides. Unlike area, you do not need the height for this calculation! Just remember that opposite sides of a parallelogram are equal in length, which makes the addition a little bit easier for you to work with.
Common Questions
What is the formula for the perimeter of a parallelogram?
The perimeter of a parallelogram is P = 2(a + b), where a and b are the lengths of the two pairs of opposite sides. Since opposite sides are equal, you add one of each side length and multiply by 2.
Why does the parallelogram perimeter formula use 2(a + b)?
A parallelogram has two pairs of equal parallel sides. Adding the two different side lengths and multiplying by 2 accounts for all four sides efficiently.
Is the perimeter formula for a rectangle the same as for a parallelogram?
Yes. A rectangle is a special parallelogram, so both use P = 2(l + w) or equivalently P = 2(a + b). The formula is identical.
How do you find a missing side of a parallelogram if you know the perimeter?
Substitute the known values into P = 2(a + b) and solve for the unknown side by applying inverse operations.
Where is perimeter of a parallelogram taught in Grade 8?
Perimeter of a parallelogram is covered in Saxon Math Course 3, Chapter 6: Number and Operations and Data Analysis and Probability.