GEOpart2

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Slide1:

The A,B,C’s of Geometry- PART 2 4 th grade Perimeter, Area, Circles + Geometry Problems

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Perimeter & Area o f Squares & Rectangles Area m easures the distance around. Perimeter m easures all the space inside.

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Perimeter o f Squares & Rectangles m easures the distance around. Perimeter If you walk around the 4 sides of a soccer field, then you’ve walked the perimeter. To calculate the PERIMETER , measure the 4 sides and add them together. Perimeter = side1 + side2 + side3 + side4

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Perimeter = side1 + side2 + side3 + side4 If a soccer field is 120 feet long and 80 feet wide , what is the perimeter ? 120 feet 120 feet 80 feet 80 feet P = s1 + s2 + s3 + s4 P = 120 + 80 + 120 + 80 P = 400 feet

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Perimeter & Area o f Squares & Rectangles Area m easures the distance around. Perimeter m easures the space inside. Got it But how do I measure the space inside?

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Area o f Squares & Rectangles Make a “mathematical” d rawing like this one Fill your soccer field with squares to make a grid .

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120 feet 80 feet LENGTH W I D T H 120 feet 80 feet 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Each square in the grid contains 400 square feet (20x20) . There are 24 squares , so the whole soccer field contains 9,600 square feet (24 x 400 = 9,600). 400 Area = Length x Width Calculate the AREA like this: A = L x W A = 120 x 80 A = 9,600 square feet When two dimensions are multiplied, they produce a “squared” measurement. Understanding the grid : 20 20 20 20 20 20 = 120 20 20 20 20 = 80

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Perimeter & Area o f Squares & Rectangles LENGTH W I D T H 120 feet 80 feet Perimeter around equals 400 feet. Area inside equals 9,600 square feet. Is it possible for the Perimeter and the Area to be the same number ? YES, but the Area will always be a squared measure ! 4 inches 4 inches 4 inches 4 inches Perimeter = 4 + 4 + 4 + 4 = 16 inches Area = 4 x 4 = 16 square inches Soccer Field

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Perimeter & Area o f Squares & Rectangles Area m easures the distance around. i s a line (linear) measurement. Perimeter m easures the space inside. i s a squared measurement. x + ❶ ❷ ❶ In Summary…

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Circles Radius Diameter Center 1/4 90° 1/4 90° 90° 90° 1/4 1/4 Each ¼ of a circle contains 90 °. A full circle contains 360°.

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Practice & Extension Q1. Why can’t we name this ray BA? Q2. Why can we name this revised ray BA?

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Q3. What is the name of this ray: Ray BA or Ray AB? A. Remember: the ENDPOINT is always the first point in the name of a ray. So the only answer is Ray AB. Q4. What is the correct way to write the name of this ray: AB or AB? A. Remember: the ARROW always points to the right. So the only answer is:

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Q5 How would you describe these two lines: intersecting or perpendicular ? Q6. What does this symbol mean? This symbol represents a 90° angle. If the two lines cross at a 90 degree angle, then they are perpendicular to each other.

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Q7. How would you describe these two lines: intersecting or parallel ? Remember: intersecting means that they cross over each other, and parallel means that they never touch. A. To answer this question, make the lines longer. Now you see that they will cross each other. So, they are intersecting lines , not parallel.

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8 . What do the symbols in the middle mean? A . This symbol means parallel . This symbol means perpendicular . Q9. What kind of angle is this? Acute, Right, or Obtuse? Q10. What is its measure? 45° 90° or 100°

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Q11. What does Angle CDE measure? 45 ° 90° or 100 ° Q12. What kind of angle is Angle D? A. Acute, right, or obtuse? C D E Q13. If you had to guess, what is the measure of Angle Q? 85° 95° or 175° Q R P C

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Q14. What is the measure of the angle formed by: T he orange ray? 6 5° 75° The green ray? A. 125 ° 135 ° Angles “open up” from 0° 0° can be on the right or left side of a protractor.

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Q15. What kind of angle is formed by the clock’s hands? A. Acute, right, or obtuse? 60° Q16. What is the size of this angle? A. 60°, 120° or 135°

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12 cm 12 cm Q17. What is the perimeter of the square? A. 24 centimeters, 36 cm, 48 cm Q18. What is the area of the square? A. 48 cm, 108 cm, 144 cm Q19. Why are none of the answers to Q18 correct? a. Because the real answer is 60 cm. b. Because the real answer must be stated as square cm Q20. What are the ways that you can show squared in your answer? s quare centimeters, sq. cm, a ll are correct!

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Q21. For each activity below, what needs to be measured: the perimeter or the area ? New carpet for the bedroom New lines around the football field New paint for the classroom walls A new fence around the grassy field New paper to cover the bulletin board at school New tile on the kitchen floor P A P A

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(acute angle) (parallelogram) (right triangle) (area of a rectangle)

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