Use with Ready Instruction Lesson 21
Dear Family,
Your child is learning about area and
circumference of a circle.
Area is the amount of space inside a circle.
Circumference is the distance around a circle.
The radius, r, is the distance from the center of a
circle to any point on the circle. The diameter, d, is
the distance across the center of a circle. It is twice
as long as the radius.
A special relationship exists between the
circumference of a circle and its diameter. The ratio
of the circumference to the diameter is always the
same, no matter what size the circle is.
The letter C
stands for
circumference.
C
d
r
  
   
​ 5 p ø ​ 22  ​ ø 3.14
​ circumference
diameter
···········
7
··
The symbol p is pronounced “pi.” The decimal 3.14 and the fraction ​ 22  ​
are commonly used approximations for p. The formulas for the area
7
··
and circumference of a circle involve p.
Area: A 5 pr2Circumference: C 5 pd
Consider this situation:
A circular stained glass window is set
in a square frame. The frame is
18 inches long on each side. What is
the circumference of the window?
What is the area of the window?
The next page shows how your child might find the circumference and
the area of the stained glass window.
©Curriculum Associates, LLC Copying is not permitted.
Lesson 21 Area and Circumference of a Circle
217
Area and Circumference of a Circle: Sample Solution
A circular stained glass window is set in a square frame. The
frame is 18 inches on a side. What is the circumference of the
stained glass window? What is its area?
Find the circumference:
Use a diagram and a formula to find the circumference
of the window.
The length of the diameter of the circle is equal to the
side length of the square, 18 inches.
Use the formula for the circumference of a circle.
Use 3.14 for p.
18 in.
C 5 pd
5 3.14(18)
5 56.52
The circumference is 56.52 inches.
Find the area:
Use a diagram and a formula to find the area of
the window.
The diameter of a circle is twice as long as its radius.
The diameter is 18 inches, so the radius is 9 inches.
Use the formula for the area of a circle. Use 3.14 for p.
A 5 pr2
5 3.14(92)
5 3.14(81)
5 254.34
18 in.
The area is 254.34 square inches.
Answer: The circumference of the stained glass window is
56.52 inches, and the area is 254.34 square inches.
218
Lesson 21 Area and Circumference of a Circle
©Curriculum Associates, LLC Copying is not permitted.