# 6.7 - Area, Perimeter, Circumference

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.

### 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

·  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

·  6.7a1  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.

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

·  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: Nov 20, 2018