11.1 Understanding Area. Units of measure 1.Linear units: perimeter, circumference 2.Square units: area 3.Cubic units: volume Definition: The area of.

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Presentation transcript:

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 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. A sq = s 2 Where s is the length of a side.

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. A B C D E F L M NQ OP

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. = +

To solve these problems: 1.Write the correct formula 2.Plug in the correct numbers 3.Compute and give answer with correct units. (minimum 3 lines!) 4.For irregular shapes, divide it into individual shapes, solve each shape and then add together.

Example: Find the area of the shape below. 3m 13m 8m 1.Divide the shape into 3 rectangles. 2.Find the area of each rectangle. 3.Add the areas together. Method 1

3m 13m 8m A = bh + bh + bh = 3(8) + 14(13) + 3(8) = = 230m 2

3m 13m 8m Method 2 1.Calculate the base and height of the original rectangle, find total area. 2.Calculate the area of the 4 corners. 3.Subtract the 4 corners from the total area.

3m 13m 8m A = bh-4s 2 = 19(14) - 4(3) 2 = = 230m 2

Find the area of the walkway around the pool. 40ft 35ft 38ft 30ft Area of the whole: A = bh = 40(35) = 1400 ft 2 Area of the Pool : A = bh = 30(38) = 1140 ft 2 Area of the walkway: 1400 ft 2 – 1140 ft 2 = 260 ft 2

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!