Perimeter

Definition

Perimeter is the distance around the outer boundary or edge of a two-dimensional geometric shape. It is the sum of the lengths of all the sides that enclose a particular region.

5 Must Know Facts For Your Next Test

1. The perimeter of a rectangle is calculated by adding the lengths of all four sides.
2. For a triangle, the perimeter is the sum of the lengths of the three sides.
3. The perimeter of a trapezoid is found by adding the lengths of the two parallel bases and the two non-parallel sides.
4. Perimeter is an important concept in construction, landscaping, and other real-world applications that involve measuring the boundaries of a space.
5. Knowing the perimeter of a shape can be useful for calculating the amount of fencing, edging, or other materials needed to enclose an area.

Review Questions

• How is the perimeter of a rectangle calculated?
  • The perimeter of a rectangle is calculated by adding the lengths of all four sides. Specifically, the formula for the perimeter of a rectangle is: $P = 2l + 2w$, where $l$ is the length and $w$ is the width of the rectangle. This formula works because rectangles have two pairs of equal sides, so the perimeter can be found by doubling the sum of the length and width.
• Explain how the perimeter of a triangle differs from the perimeter of a rectangle or trapezoid.
  • The perimeter of a triangle is calculated by adding the lengths of its three sides, whereas the perimeter of a rectangle or trapezoid involves adding the lengths of four sides. This is because a triangle is a three-sided polygon, while a rectangle and trapezoid are four-sided polygons. The formula for the perimeter of a triangle is simply the sum of its side lengths: $P = a + b + c$, where $a$, $b$, and $c$ are the lengths of the three sides. This direct summation approach differs from the more complex calculations required for the perimeter of shapes with four or more sides.
• Describe how the perimeter of a trapezoid is related to the properties of rectangles and triangles.
  • The perimeter of a trapezoid can be calculated by adding the lengths of its two parallel bases and its two non-parallel sides. This formula, $P = a + b + c + d$, where $a$ and $b$ are the lengths of the parallel bases and $c$ and $d$ are the lengths of the non-parallel sides, combines the properties of rectangles (with two parallel sides) and triangles (with three non-parallel sides). The perimeter of a trapezoid is therefore a hybrid of the perimeter calculations for these other fundamental geometric shapes, highlighting the connections between the properties of different polygons.

Related terms

Polygon: A closed two-dimensional shape made up of straight line segments.

Circumference:

The distance around the outside of a circular shape, such as a circle or ellipse.

Area:

The measurement of the space enclosed within the boundaries of a two-dimensional shape.