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Lesson 19

Lesson 19. Perimeter, Area, Volume. 8 ft. 4 ft. 8 ft. Some GEPA questions apply percent to areas of squares and circles. This shows the interrelationship of percent, algebra, and geometry, as illustrated in the following example. Example 1:

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Lesson 19

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  1. Lesson 19 Perimeter, Area, Volume

  2. 8 ft. 4 ft. 8 ft. Some GEPA questions apply percent to areas of squares and circles. This shows the interrelationship of percent, algebra, and geometry, as illustrated in the following example. Example 1: What is the best estimate of the shaded portion on the diagram below? A. 10% B. 20% C. 40% D. 80%

  3. This is equivalent to solving the following problem: The area of the circle is what percent of the area of the square? 1. Find the area of the circle. Use A = pi * r2 4 ft. A = pi * r2 A = 3.14 * 2ft * 2ft A = 3.14 * 4ft2 A = 12.56 ft2 radius 2ft . you're not done yet!

  4. 2. Find the area of the square. Use A = s2 A = s2 A = 8ft * 8ft A = 64 ft2 8ft 8ft

  5. 3. Write an equation: Area of circle is what percent of area of square? 12.56 ft2 = x 64 * 12.56 ft2 = 64 x (divide each side by 64) = x 0.19625 Round 0.19625 to 0.20. Write as percent : 20%

  6. 200 ft. 50 ft. The next application involves the distance around a circle: circumference of a circle. The formula for the circumference of a circle : C = 2 * pi * r Example 2: The diagram below represents a racetrack in the shape of a rectangle with a semicircle at each end. Find the total distance around the track.

  7. 200 ft. 50 ft. 200 ft. 50 ft. 25 ft. The total distance around the track is: 200 ft + 200 ft + distance around each semicircle. Separate the two semicircles from the rectangle. Put them together to get the whole Circle with radius 25 ft. Distance around track is: 200 ft + 200 ft + circumference of circle 200 ft + 200 ft + 2 * pi * r 200 ft + 200 ft + 2 * 3.14 * 25 ft 200 ft + 200 ft + (50 * 3.14) ft 400 ft + 157 ft = 557 ft

  8. 1 yd 3 ft 1 yd 3 ft Sometimes the area of a more complex figure can be found by breaking it up into several rectangles or squares. Then the area of the original figures will be the sum of the areas of the smaller rectangles and squares. First of all, note that the cost of carpeting a room is computed for the number of square yards of area, NOT the number of square feet. Recall that 3 ft = 1 yd. or So, from the drawing at the right, 1 yd2 = 9 ft2 1 square yard = 9 square feet 1 * yd * 1 * yd = 3 * ft * 3 * ft 1 yd2 = 9 ft2

  9. Example 3: The floor plan below shows the measurements of a living room in feet. Find the minimum number of square yards of carpeting needed to carpet the entire floor wall to wall. A. 27 yards2 B. 28 yards2 C. 248 yards2 D. 298 yards2 16 1. Find the missing side lengths 18 10 12

  10. Example 3: The floor plan below shows the measurements of a living room in feet. Find the minimum number of square yards of carpeting needed to carpet the entire floor wall to wall. A. 27 yards2 B. 28 yards2 C. 248 yards2 D. 298 yards2 16 8 1. Find the missing side lengths 18 4 10 12

  11. Example 3: The floor plan below shows the measurements of a living room in feet. Find the minimum number of square yards of carpeting needed to carpet the entire floor wall to wall. A. 27 yards2 B. 28 yards2 C. 248 yards2 D. 298 yards2 16 8 1. Find the missing side lengths 18 2. Separate the figure into 2 rectangles. 4 10 12

  12. 16 8 8 18 4 4 10 12 12 Separate the figure into 2 rectangles. 8 x 16 = 128 10 x 12 = 120 12 x 18 = 216 8 x 4 = 32 Total area = 32 + 216 = 248 Total area = 128 + 120 = 248 you're not done yet!

  13. Total area = 128 + 120 = 248 This is the area in square feet. Convert this to square yards, since that is what is called for in the problem. There are 9 square feet in one square yard. Find how many 9’s there are in 248. Divide : 248 ÷ 9 = 27.55555556 The carpet store can not give you a decimal or fraction part of a yard, You need the next higher whole number of yards : 28. 28 yd2

  14. VOLUME The formula for volume : V = L * W * H Example: What is the volume of a rectangle solid measuring 12 cm wide by 7 cm long by 4 cm high? V = L * W * H V = 12 * 7 * 4 * cm * cm *cm V = 336 cm3

  15. Mr. Miller has 640 ft3 of water in his in ground pool. The pool is 4 ft deep (high) and 20 ft long. How wide is the pool? A. 8 ft B. 24 ft C. 80 ft D. 160 ft Since 640 ft3 indicates volume, use the volume formula to write an equation. V = L * W * H 640 = * 4 20 * W (divide each side by 80) 640 = 80W 8 = W

  16. 3 cm 5 cm 4 cm Surface Area The total surface area of a rectangle solid is the sum of the areas of the 6 faces, or double the area of the 3 faces you can see. Example: Find the total surface area of the rectangular solid. A. 27 cm2 B. 47 cm2 C. 60 cm2 D 94 cm2

  17. 3 cm 3 cm 3 cm 4 cm 5 cm 5 cm 4 cm 5 cm 4 cm Surface Area The total surface area of a rectangle solid is the sum of the areas of the 6 faces, or double the area of the 3 faces you can see. Example: Find the total surface area of the rectangular solid. A. 27 cm2 B. 47 cm2 C. 60 cm2 D 94 cm2 A = 2 * (3 cm * 4 cm) + 2 * (4 cm * 5 cm) + 2 * ( 5 cm * 3 cm) A = 94 cm2

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