Perimeter

Definition

Perimeter is the distance around the outer boundary or edge of a two-dimensional geometric shape. It is a fundamental concept in geometry that is essential for understanding and solving various applications involving triangles, rectangles, and the Pythagorean Theorem.

5 Must Know Facts For Your Next Test

1. The perimeter of a triangle is the sum of the lengths of its three sides.
2. The perimeter of a rectangle is the sum of twice the length and twice the width.
3. The Pythagorean Theorem can be used to calculate the length of the third side of a right triangle, which is then used to determine the perimeter.
4. Perimeter is an important concept in various real-world applications, such as calculating the amount of fencing or edging needed for a garden or the length of a running track.
5. Knowing the perimeter of a shape can be useful in determining the amount of material needed for a project, such as the length of tile or carpet required to cover a floor.

Review Questions

• How is the perimeter of a triangle calculated, and how does this relate to the Pythagorean Theorem?
  • The perimeter of a triangle is the sum of the lengths of its three sides. In the context of the Pythagorean Theorem, if the triangle is a right triangle, the length of the third side can be calculated using the Pythagorean Theorem. Once all three side lengths are known, the perimeter can be determined by adding them together. This relationship between the Pythagorean Theorem and the perimeter of a triangle is important for solving various geometric applications.
• Explain how the perimeter of a rectangle is calculated and how it can be used to solve real-world problems.
  • The perimeter of a rectangle is calculated by adding the lengths of all four sides, which is equivalent to twice the length plus twice the width (2L + 2W). Knowing the perimeter of a rectangle can be useful in a variety of real-world applications, such as determining the amount of fencing or edging needed for a garden or the length of a running track. By understanding the relationship between the dimensions of a rectangle and its perimeter, you can solve problems involving the efficient use of materials or the design of spaces with specific boundary requirements.
• Analyze how the concept of perimeter can be applied to solve problems involving the Pythagorean Theorem and the properties of triangles and rectangles.
  • The concept of perimeter is closely tied to the properties of triangles and rectangles, as well as the Pythagorean Theorem. For triangles, the perimeter is the sum of the lengths of the three sides, and the Pythagorean Theorem can be used to calculate the length of the third side of a right triangle, which is then used to determine the perimeter. For rectangles, the perimeter is calculated by adding the lengths of the four sides, which is directly related to the length and width of the rectangle. By understanding how to apply the formulas for perimeter and the Pythagorean Theorem, you can solve a wide range of geometric problems involving the dimensions and measurements of these shapes, such as determining the amount of fencing or materials needed for a project or analyzing the properties of various geometric structures.

Related terms

Circumference: The distance around the outer edge of a circular shape, such as a circle or a cylinder.

Area: The measure of the two-dimensional space enclosed within the boundaries of a geometric shape.

Polygon: A closed, two-dimensional shape made up of straight line segments, such as triangles, rectangles, and other polygons.