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11.1 Understanding Area

11.1 Understanding Area. Objective: After studying this section you will be able to understand the concept of area, find the areas of rectangles and squares and use the basic properties of area. The Concept of Area.

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11.1 Understanding Area

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  1. 11.1 Understanding Area Objective: After studying this section you will be able to understand the concept of area, find the areas of rectangles and squares and use the basic properties of area.

  2. The Concept of Area We measure lengths of line segments in linear units. It could be in meters, yards, miles, centimeters, etc. one square unit The standard units of area or square units such as square meters, square yards, square miles, etc. one linear unit A square mile is the area is the space enclose by a square whose sides are each one mile in length. Definition The area of a closed region is the number of square units of space within the boundary of the region

  3. We can estimate the area of a region by determining the approximate number of square units it would take to fill the region. estimated area = 24 sq units estimated area =? estimated area = 16 sq units

  4. Counting squares is neither the easiest or the best way to find the area of a region. Let’s investigate how to find the areas of rectangles and squares We could count them However, that is not the most efficient use of our time. Any ideas on how to calculate this in a more timely fashion? We could multiply the number of columns (base) by the number of rows (height)

  5. Postulate The area of a rectangle is equal to the product of the base and the height for that base. where b is the length of the base and h is the height In a square, the base and the height are equal. Theorem 99 The area of a square is equal to the square of a side. where s is the length of a side.

  6. A G F L E K J D H B C I Basic Properties of Area Postulate Every closed region has an area. Postulate If two closed figures are congruent, then their areas are equal. 1 Then the area of region 1 is congruent to the region of area 2. 2

  7. Postulate If two closed regions intersect only along a common boundary, then the area of their union is equal to the sum of their individual areas. = +

  8. Example 1 Find the area of the rectangle 13 cm 5 cm Example 2 Given that the area of a rectangle is 20 sq dm and the altitude is 5 dm, find the base. (Hint: draw a picture)

  9. Example 3 Find the area of the green shaded region 2 2 2 6 5 7 3

  10. Summary Summarize the postulates you learned about today. Homework: worksheet

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