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5-Minute Check 4

A B C D. 160. 5-Minute Check 4. A B C D. Write an equation of the circle with center at (–3, 2) and a diameter of 6. ( x + 3) 2 + ( y – 2) 2 = 9. 5-Minute Check 5. A B C D.

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5-Minute Check 4

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  1. A B C D 160 5-Minute Check 4

  2. A B C D Write an equation of the circle with center at (–3, 2) and a diameter of 6. (x + 3)2 + (y – 2)2 = 9 5-Minute Check 5

  3. A B C D Which of the following figures is always perpendicular to a radius of a circle at their intersection on the circle? A. chord B. diameter C. secant D. tangent 5-Minute Check 6

  4. Find perimeters and areas of parallelograms. • Find perimeters and areas of triangles. Then/Now

  5. Concept 1

  6. Concept 2

  7. Find the perimeter and area of Perimeter Since opposite sides of a parallelogram are congruent, RSUT and RUST. So UT = 32 in. and ST = 20 in. Perimeter and Area of a Parallelogram Example 1

  8. Perimeter and Area of a Parallelogram Perimeter = RS + ST + UT + RU = 32 + 20 + 32 + 20 = 104 in. AreaFind the height of the parallelogram. The height forms a right triangle with points S and T with base 12 in. and hypotenuse 20 in. c2 = a2 + b2 Pythagorean Theorem 202 = 122 + b2c = 20 and a = 12 400 = 144 + b2 Simplify. Example 1

  9. The height is 16 in. UT is the base, which measures 32 in. Perimeter and Area of a Parallelogram 256 = b2 Subtract 144 from each side. 16 = b Take the positive square root of each side. A = bh Area of parallelogram = (32)(16) or 512 in2b = 32 and h = 16 Answer: The perimeter is 104 in. and the area is 512 in2. Example 1

  10. A B C D A. Find the perimeter and area of 88 m; 405 m2 Example 1

  11. Find the area of Area of a Parallelogram Step 1 Use a 45°-45°-90° triangle to find the height h of the parallelogram. Example 2

  12. Recall that if the measure of the leg opposite the 45° angle is h, then the measure of the hypotenuse is Divide each side by . Area of a Parallelogram Substitute 9 for the measure of the hypotenuse. ≈ 6.36 Simplify. Example 2

  13. Area of a Parallelogram Step 2 Find the area. A = bh Area of a parallelogram ≈ (12)(6.36)b = 12 and h = 6.36 ≈ 76.3 Multiply. Answer: 76.3 square units Example 2

  14. A B C D Find the area of 135.76 cm2 Example 2

  15. Concept 3

  16. Concept 4

  17. Perimeter and Area of a Triangle SANDBOXYou need to buy enough boards to make the frame of the triangular sandbox shown and enough sand to fill it. If one board is 3 feet long and one bag of sand fills 9 square feet of the sandbox, how many boards and bags do you need to buy? Example 3

  18. Perimeter and Area of a Triangle Step 1 Find the perimeter of the sandbox. Perimeter = 16 + 12 + 7.5 or 35.5 ft Step 2 Find the area of the sandbox. Area of a triangle b = 12 and h = 9 Example 3

  19. boards Perimeter and Area of a Triangle Step 3 Use unit analysis to determine how many of each item are needed. Boards Bags of Sand Example 3

  20. Perimeter and Area of a Triangle Round the number of boards up so there is enough wood. Answer: You will need 12 boards and 6 bags of sand. Example 3

  21. A B C D PLAYGROUNDYou need to buy enough boards to make the frame of the triangular playground shown here and enough mulch to fill it. If one board is 4 feet long and one bag of mulch covers 7 square feet, how many boards and bags do you need to buy? 12 boards and 14 bags of mulch Example 3

  22. Use Area to Find Missing Measures ALGEBRA The height of a triangle is 7 inches more than its base. The area of the triangle is 60 square inches. Find the base and height. Step 1 Write an expression to represent each measure. Let b represent the base of the triangle. Then the height is b + 7. Step 2 Use the formula for the area of a triangle to find b. Area of a triangle Example 4

  23. Use Area to Find Missing Measures Substitution 120 = (b)(b + 7) Multiply each side by 2. 120 = b2 + 7b Distributive Property 0 = b2 + 7b – 120 Subtract 120 from each side. 0 = (b – 8)(b + 15) Factor. b – 8 = 0 and b + 15 = 0 Zero Product Property b = 8 b = –15 Solve for b. Example 4

  24. Use Area to Find Missing Measures Step 3 Use the expressions from Step 1 to find each measure. Since a length cannot be negative, the base measures 8 inches and the height measures 8 + 7 or 15 inches. Answer:b = 8 in., h = 15 in. Example 4

  25. A B C D ALGEBRAThe height of a triangle is 12 inches more than its base. The area of the triangle is 560 square inches. Find the base and the height. base = 28 in. and height = 40 in. Example 4

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