Circles

• area of a figure is defined as the number of unit squares that cover the surface of it
• perimeter measures the total length of the edges of a closed plane figure
• a circle has no base, height, or an edge
• area of a circle

  $\pi r^2$
• circumference of a circle

  $2 \pi r$
• The word circumference comes from the Latin words circum (which means “around”), and ferre (which means “to carry”).
• Circumference is the counterpart of perimeter in a circle.
• area of a semicircle

  $1/2 \pi r^2$
• An arc is a continuous part of a circle
• There are three classifications of an arc – a minor arc, a major arc, and a semicircle.
• A semicircle is an arc measuring one-half the circumference of a circle
• If we are going to describe arc length as the length of the string that is laid along an arc, what is the length of the string laid around the entire circle?

  The circumference, 2πr
• arc length formula

  $(x/360) 2 \pi r$
• any circle of radius r and central angle θ in radians has an arc length S given by the formula

  $S =$$\theta r$
• A sector of a circle is a region bounded by two radii and their intercepted arc.
• The area of the sector is proportional to the angle that the arc subtends at the center. This is what we call the central angle or the sector angle.
• area of a sector formula

  $(\theta/360) \pi r^2$