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Understanding Area Lesson 11.1 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: Arect = bh where b is the length of the base and h is the length of the height. Theorem 99: the area of a square is equal to the square of a side. Asq = s2 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. L B A 1 F E C D M 2 Q P N O 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. 13m 3m 3m 8m 3m 3m Method 1 1. Divide the shape into 3 rectangles. 2. Find the area of each rectangle. 3. Add the areas together. 13m 3m 3m 8m 3m 3m A = bh + bh + bh = 3(8) + 14(13) + 3(8) = 24 + 182 + 24 = 230m2 13m 3m 3m 8m 3m 3m 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. 13m 3m 3m 8m 3m 3m A = bh-4s2 = 19(14) - 4(3)2 = 266 - 36 = 230m2 40ft 30ft 38ft 35ft Find the area of the walkway around the pool. A = bh – bh A = 40(35) – 38(30) A = 1400 – 1140 A = 260 ft2 Time to Paint the Classroom… This classroom could use a fresh coat of paint. With your team, determine how many square feet will need to be painted. Keep your calculations secret until we reveal them to the class.