Section 13.2: Perimeters of Composite Figures

Property

Perimeter is the distance around the outside of a shape. It is measured in linear units (like feet, meters, or inches) and represents the total length of all the sides or boundaries of a figure.

Examples

Property

When estimating perimeter on grid paper: horizontal and vertical segments = $1$ unit each, diagonal segments ≈ $1.5$ units each.

Examples

Property

The perimeter of a composite figure includes only the outer edges that form the boundary of the entire shape. Interior edges where component shapes connect are not part of the perimeter calculation.

Examples

Property

From the relationship $A = \frac{1}{2}Cr$ and $A = \pi r^2$, we can derive the formula for the circumference of a circle in terms of its radius $r$:

Examples

• A bicycle wheel has a radius of $12$ inches. The distance it travels in one full rotation is its circumference: $C = 2\pi(12) = 24\pi$ inches.
• The circumference of a circular pool is $40\pi$ feet. To find its diameter, we can use the formula $C = \pi d$. So, $40\pi = \pi d$, which means the diameter is $40$ feet.
• A hula hoop has a radius of $50$ cm. Its circumference is calculated as $C = 2\pi(50) = 100\pi$ cm.

Explanation

The circumference is the distance around a circle. It's always a little more than three times the distance across the circle (the diameter). This 'a little more than three' is exactly $2\pi$ times the radius, making $\pi$ the key conversion factor.