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11.1 Understanding Area

11.1 Understanding Area. Units of measure 1.Linear units: perimeter, circumference 2.Square units: area 3.Cubic units: volume. Definition: The area of a closed region is the number of square units of space within the boundary of the region. Area of a rectangle: A rect = bh

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11.1 Understanding Area

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  1. 11.1 Understanding Area

  2. Units of measure 1.Linear units: perimeter, circumference 2.Square units: area 3.Cubic units: volume Definition: The area of a closed region is the number of square units of space within the boundary of the region.

  3. Area of a rectangle: Arect = bh Where b is the length of the base and h is the length of the height. T99: the area of a square is equal to the square of a side. Asq = s2 Where s is the length of a side.

  4. Postulate: every closed region has an area. If two closed figures are congruent, then their areas are equal. If ABCDEF is congruent to LMNOPQ, then the area of region 1 is equal to the area of region 2. L M B A F Q N C D P O E

  5. 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. + =

  6. To solve these problems: Write the correct formula Plug in the correct numbers Compute and give answer with correct units. (minimum 3 lines!) For irregular shapes, divide it into individual shapes, solve each shape and then add together.

  7. 13m 3m 3m 8m 3m 3m Example: Find the area of the shape below. Method 1 Divide the shape into 3 rectangles. Find the area of each rectangle. Add the areas together.

  8. 13m 3m 3m 8m 3m 3m A = bh + bh + bh = 3(8) + 14(13) + 3(8) = 24 + 182 + 24 = 230m2

  9. 13m 3m 3m 8m 3m 3m Method 2 Calculate the base and height of the original rectangle, find total area. Calculate the area of the 4 corners. Subtract the 4 corners from the total area.

  10. 13m 3m 3m 8m 3m 3m A = bh-4s2 = 19(14) - 4(3)2 = 266 - 36 = 230m2

  11. 40ft Find the area of the walkway around the pool. 30ft 35ft 38ft Area of the whole: A = bh = 40(35) = 1400 ft2 Area of the Pool : A = bh = 30(38) = 1140 ft2 Area of the walkway: 1400 ft2 – 1140 ft2 = 260 ft2

  12. Assignment: Make your own area problem! Come up with something creative that involves several different shapes. Write a rough draft and then a final draft on the construction paper. You have 15 minutes to come up with the problem When finished: Pass your problem to the person behind you to calculate the area!

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