Perimeter and Circumference in Geometry

Questions and Answers

What is the term used to describe the distance around a circle?

Radius

Diameter

Circumference (correct)

Perimeter

What is a characteristic of a regular polygon?

It is a three-dimensional shape

All angles are of equal measure (correct)

All sides are of unequal length

It has fewer than three sides

What is the formula to find the perimeter of a regular polygon?

n + a

n - a

n / a

n × a (correct)

What is the meaning of the prefix 'peri-' in the word perimeter?

Around Signup and view all the answers

What type of polygon is a square?

Regular polygon Signup and view all the answers

What units are used to measure perimeter and circumference?

Linear units Signup and view all the answers

What is an irregular polygon?

A polygon that is not regular, meaning it is not equilateral or equiangular Signup and view all the answers

What is the formula to find the perimeter of an irregular polygon?

P = s × n Signup and view all the answers

What is the perimeter of an equilateral triangle with a side length of 9 units?

36 units Signup and view all the answers

What is the perimeter of a square with a side length of 6 units?

24 units Signup and view all the answers

What is the formula to find the perimeter of a rectangle?

P = 2(l + w) Signup and view all the answers

What is the circumference of a circle with a radius of 12 units?

40.82 units Signup and view all the answers

What is a characteristic of an equilateral triangle?

All sides are congruent Signup and view all the answers

What is a type of irregular polygon?

L-shaped polygon Signup and view all the answers

What is the center of a circle?

A point equidistant from any point on the circle Signup and view all the answers

Study Notes

Perimeter and Circumference

Perimeter is the measure of the distance or path around a 2D geometric shape, particularly polygons.
Polygons are closed, 2D shapes with at least three straight sides and three angles.
Circles are not considered to be polygons, and the distance around a circle is called the circumference.
Perimeter and circumference both measure the distance around a geometric shape and are measured in linear units (e.g., inches, feet, meters, kilometers).

Types of Polygons

Regular polygons are equilateral and equiangular, meaning all sides are equal in length and all angles are equal in measure.
Irregular polygons are not regular, meaning they are not equilateral or equiangular.
Examples of regular polygons include squares and equilateral triangles.
Examples of irregular polygons include concave polygons with unequal sides and angles.

Finding Perimeter

The formula for finding the perimeter of a regular polygon is P = n * a, where n is the number of sides and a is the length of one side.
The universal formula for finding the perimeter of any polygon (regular or irregular) is P = ∑_side lengths.
The formula can be used to find the perimeter of irregular polygons, such as concave L-shaped polygons.

Perimeter of Specific Shapes

The perimeter of an equilateral triangle is found by multiplying the length of one side by 3 (P = 3 * s).
The perimeter of a square is found by multiplying the length of one side by 4 (P = 4 * s).
The perimeter of a rectangle is found by adding the length and width, and then multiplying by 2 (P = 2 * (l + w)).

Circumference of a Circle

The circumference of a circle is found using the formula C = 2 * π * r, where r is the radius of the circle.
The radius is the distance from the center of the circle to any point on the circle's outline.