# 6.10abc and *6.7 - Area, Perimeter, Circumference

6.10abc    The student will

a)  define pi (π) as the ratio of the circumference of a circle to its diameter;

b)  solve practical problems involving circumference and area of a circle, given the diameter or radius;

c) solve practical problems involving area and perimeter;

6.7  The student will

a)  derive π (pi);

b)  solve problems, including practical problems, involving circumference and area of a circle; and

c)  solve problems, including practical problems, involving area and perimeter of triangles and rectangles.

Bloom's Level:  Remember, Apply

### BIG IDEAS

• I can make a tent by determining the square feet of canvas needed for 4 walls and floor, how much netting is needed for the door, and how long a zipper will surround the door opening.
• I will be able to find area, perimeter, circumference, and surface area as appropriate in various situations.

### UNDERSTANDING THE STANDARD

• Experiences in deriving the formulas for area, perimeter, and volume using manipulatives such as tiles, one-inch cubes, adding machine tape, graph paper, geoboards, or tracing paper, promote an understanding of the formulas and facility in their use.†
• The perimeter of a polygon is the measure of the distance around the polygon.
• Circumference is the distance around or perimeter of a circle.
• The area of a closed curve is the number of nonoverlapping square units required to fill the region enclosed by the curve.
• The perimeter of a square whose side measures s is 4 times s (P = 4s), and its area is side times side  (A = s2).
• The perimeter of a rectangle is the sum of twice the length and twice the width [P = 2l + 2w, or P = 2(l + w)], and its area is the product of the length and the width (A = lw).
• The value of pi (π) is the ratio of the circumference of a circle to its diameter.
• The ratio of the circumference to the diameter of a circle is a constant value, pi (π), which can be approximated by measuring various sizes of circles.
• The fractional approximation of pi generally used is 22/7.
• The decimal approximation of pi generally used is 3.14.
• The circumference of a circle is computed using C = πd or C = 2πr, where d is the diameter and r is the radius of the circle.
• The area of a circle is computed using the formula , A = πr2 where r is the radius of the circle.
• The surface area of a rectangular prism is the sum of the areas of all six faces (SA = 2lw + 2lh + 2wh).
• The volume of a rectangular prism is computed by multiplying the area of the base, B, (length x width) by the height of the prism (V = lwh = Bh).

·  The value of pi (p) is the ratio of the circumference of a circle to its diameter. Thus, the circumference of a circle is proportional to its diameter.

·  The calculation of determining area and circumference may vary depending upon the approximation for pi. Common approximations for π include 3.14, , or the pi (p) button on a calculator.

·  Experiences in deriving the formulas for area, perimeter, and volume using manipulatives such as tiles, one-inch cubes, graph paper, geoboards, or tracing paper, promote an understanding of the formulas and their use.

·  Perimeter is the path or distance around any plane figure. The perimeter of a circle is called the circumference.

·  The circumference of a circle is about three times the measure of its diameter.

·  The circumference of a circle is computed using C = πd or C = 2πr, where d is the diameter and r is the radius of the circle.

·  The area of a closed curve is the number of nonoverlapping square units required to fill the region enclosed by the curve.

·  The area of a circle is computed using the formula A = πr2, where r is the radius of the circle.

·  The perimeter of a square whose side measures s can be determined by multiplying 4 by s (P = 4s), and its area can be determined by squaring the length of one side (A = s2).

·  The perimeter of a rectangle can be determined by computing the sum of twice the length and twice the width (P = 2l + 2w, or P = 2(l + w)), and its area can be determined by computing the product of the length and the width (A = lw).

·  The perimeter of a triangle can be determined by computing the sum of the side lengths (P = a + b +  c), and its area can be determined by computing 1/2 the product of the base and the height (A = 1/2 bh).

### ESSENTIALS

• What is the relationship between the circumference and diameter of a circle?
The circumference of a circle is about 3 times the measure of the diameter.
• What is the difference between area and perimeter? Perimeter is the distance around the outside of a figure while area is the measure of the amount of space enclosed by the perimeter.

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

6.10a1  Derive an approximation for pi by gathering data and comparing the circumference to the diameter of various circles, using concrete materials or computer models.

·  6.7a1  Derive an approximation for pi (3.14 or ) by gathering data and comparing the circumference to the diameter of various circles, using concrete materials or computer models.

6.10b1  Find the circumference of a circle by substituting a value for the diameter or the radius into the formula C = πd or C = 2πr

6.10b2  Find the area of a circle by using the formula A = π

·  6.7b1  Solve problems, including practical problems, involving circumference and area of a circle when given the length of the diameter or radius.

6.10b3  Create and solve problems that involve finding the circumference and area of a circle when given the diameter or radius.

6.10c1  Apply formulas to solve practical problems involving area and perimeter of triangles and rectangles.

·  6.7c1  Solve problems, including practical problems, involving area and perimeter of triangles and rectangles.

### KEY VOCABULARY

formula, area, perimeter, volume, polygon, circumference, closed curve, sum, twice, length, width, height, product, pi, diameter, radius, relationship, surface dimension, base

Updated: Oct 27, 2017