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Chapter 12 Measurement

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Chapter 12 Measurement

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    1. Chapter 12 Measurement Section 12.2 Measuring the Perimeter and Area of Polygons

    2. Perimeter The perimeter, P, of a polygon is the distance around the polygon or the sum of the lengths of each side of the polygon. Perimeter is a linear measurement.

    3. Common Formulas for Perimeter

    4. Area The area, A, of a polygon is the number of square units the polygon covers.

    5. A Question You have $100 to spend on fencing that costs $2.50 per foot. What is the largest area you could fence in?

    6. Activity Relating Perimeter and Area (Rectangles and Squares)

    7. Investigation Draw a rectangle whose length is 6 cm and whose width is 4 cm. Draw a second rectangle whose length is 9 cm and whose width is 6 cm. What is the relationship between these two quadrilaterals? Find the perimeter and area of each. Compare the ratios between corresponding sides, perimeters, and areas. What do you notice?

    8. Comparing Perimeters and Areas of Similar Polygons The ratio of the perimeters is the same as the ratio of any two corresponding sides (scale factor). If the scale factor of two similar polygons is a : b, then the ratio between their areas is a : b.

    9. Activity: Connecting Area of Parallelograms, Triangles, and Trapezoids On a piece of grid paper, draw a rectangle with a base of 6 cm and a height of 4cm. Find the area. What is the general formula for finding the area of a rectangle? Why? Use a colored pencil to rearrange the rectangle to make a parallelogram. Identify the base and height. How are the base and height related to the length and width of the rectangle? How are the areas related?

    10. Activity continued: What would be the formula for finding the area of a parallelogram? Draw another parallelogram. Draw a diagonal of the parallelogram. What figures are formed? How are the areas of each related? What would be the formula for finding the area of a triangle? Draw a trapezoid. Draw a diagonal of the trapezoid. How can we develop a formula for finding the area of the trapezoid by using the area of the two triangles and the distributive property?

    11. Area Formulas

    12. Area Formulas

    13. Examples Textbook: Page 691. 1.) #10 2.) #12 3.) #18 4.) #20

    14. Circumference of Circles The circumference, C, of a circle is the distance around the circle. How is circumference similar to perimeter? Different?

    15. Developing a Formula for Circumference Activity: Discovering Pi Bring in several circular objects and have students use a piece of string and a ruler to determine the circumference and diameter of each circle. Then, they will determine the ratio between the circumference and the diameter, ? !

    16. Discovering Pi

    17. Circumference of a Circle Formula ? = Circumference 3.14 or 22 Diameter 7

    18. Developing Area Formula for a Circle Draw a circle and cut it into 8 equal parts. Arrange the parts into the general shape of a parallelogram. How can this be used to arrive at the area for a circle?

    19. Area of Circle Formula

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