Understanding Area Lesson 11.1

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Presentation transcript:

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 M B A F 1 Q 2 N C D P O E

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: 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.

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

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

Calculate the area of the 4 corners. 3m 13m 8m 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.

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

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