2006 Washington State Math Championship. Unless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth.

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1 2006 Washington State Math Championship Unless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth. Geometry - Grade 5 1. How many fold rotational symmetry does the image below contain? 2. How many triangles are there in the figure below? 3. Two legs of a triangle have lengths 13 and 9. Give the range of the third leg written as an inequality with C as the variable (min<c<max) Given the Translation T(x,y) ----T (x-6,y+3) of Q(1,2), U(2,-1), A(6,-3) and D(-2,-3). 2 Q Find the sum of the x coordinates of ordered pairs of the image (the pre-image may help). -2 U 5 A D The supplement of an angle is 3 times the angle s complement. What is the missing angle?

2 6. What is the percent increase for the volume of a cube that has been dialated by a scale factor of 2? 7. A rectangle s long side is five more than twice the length of the shorter side. If the perimeter is 100, what is the length of the longest side? 8. The following geometric design is constructed by adding new squares to each rectangle. What would be the length of the longest diagonal, if the two smallest squares have side-lengths of three? 3 9. The regular hexagon below is circumscribed by a circle with a circumference of 8π. Find the shaded area. 10. The diagram shows an equiangular hexagon with sidelengths 12, 14, 18, 20, 22, 28 can be inscribed in an equilateral triangle with side-length 60. This same equiangular hexagon can also be inscribed in and equilateral triangle with side-length of n not equal to 60. What is the value on n?

3 2006 Washington State Math Championship Unless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth. Geometry - Grade 6 1. Given the Translation T(x,y) ----T (x-6,y+3) of Q(1,2), U(2,-1), A(6,-3) and D(-2,-3). 4 2 Q Find the sum of the x coordinates of ordered pairs of the image (the pre-image may help). U 5 D -2-4 A The supplement of an angle is 3 times the angle s complement. What is the missing angle? 3. What is the percent increase for the volume of a cube that has been dialated by a scale factor of 2? 4. A rectangle s long side is five more than twice the length of the shorter side. If the perimeter is 100, what is the length of the longest side? 5. The following geometric design is constructed by adding new squares to each rectangle. What would be the length of the longest diagonal, if the two smallest squares have side-lengths of three? 3 6. The regular hexagon below is circumscribed by a circle with a circumference of 8π. Find the shaded area.

4 7. The diagram shows an equiangular hexagon with side-lengths 12, 14, 18, 20, 22, 28 can be inscribed in an equilateral triangle with side-length 60. This same equiangular hexagon can also be inscribed in and equilateral triangle with side-length of n not equal to 60. What is the value on n? In 1736, the cousin of the famous Gabriel Daniel Fahrenheit, Otto Fahrenheit, invented his angle measuring scale. No rotation was 32, and half a rotation was 212. When Otto Fahrenheit measured the angles of a hexagon with his not-sofamous Fahrenheit protractor and then added them what was the sum of the angles? 9. The net (2-d drawing of a 3-d shape) of a Greenhouse is given. The 20 by 20 square is the floor of the building. If the air system circulates 8 cubic feet per second, how many minutes will it take to circulate the entire volume of the building (answer to the nearest minute)? A isosceles right triangle is removed from each corner of a square piece of paper so that a rectangle remains (each big isosceles triangle has 9 times the area of the small isosceles triangle). What is the length of the rectangle longest side, if the area sum of all 4 triangles is 200?

5 2006 Washington State Math Championship Unless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth. Geometry - Grade 7 1. A rectangle s long side is five more than twice the length of the shorter side. If the perimeter is 100, what is the length of the longest side? 2. The following geometric design is constructed by adding new squares to each rectangle. What would be the length of the longest diagonal, if the two smallest squares have sidelengths of three? 3 3. The regular hexagon below is circumscribed by a circle with a circumference of 8π. Find the shaded area. 4. The diagram shows an equiangular hexagon with side-lengths 12, 14, 18, 20, 22, 28 can be inscribed in an equilateral triangle with side-length 60. This same equiangular hexagon can also be inscribed in and equilateral triangle with side-length of n not equal to 60. What is the value on n In 1736, the cousin of the famous Gabriel Daniel Fahrenheit, Otto Fahrenheit, invented his angle measuring scale. No rotation was 32, and half a rotation was 212. When Otto Fahrenheit measured the angles of a hexagon with his not-sofamous Fahrenheit protractor and then added them what was the sum of the angles?

6 10 6. The net (2-d drawing of a 3-d shape) of a Greenhouse is given. The 20 by 20 square is the floor of the building. If the air system circulates 8 cubic feet per second, how many minutes will it take to circulate the entire volume of the building (answer to the nearest minute)? A isosceles right triangle is removed from each corner of a square piece of paper so that a rectangle remains (each big isosceles triangle has 9 times the area of the small isosceles triangle). What is the length of the rectangle longest side, if area the sum of all 4 triangles is 200? 8. Steps are made first with frames and then cement is poured into the frames. You do not need to make bottoms on the frames. Below are the 2 ft dimensions of the frames. What is the cost of making the steps given the prices below and if all boards must be one piece? 6 in Boards cost = $9 for 6 feet sections, 6 inches wide Cement cost = $6 for 4 cubic feet bags 6 in 4 ft 4 ft 9. Mr. Mo Lawnmower wants to cut out the grass triangular sections along the back of his house so he can plant some shrubs. However, feels bad about Fido (his dog) losing 120 ft some of his grass. Mr. Lawnmower vows to replace every square foot lost to the flowerbeds 60 ft 40 ft back onto the section of the very backyard. How x long will the new narrower section (40 ft wide) 20 ft'' become if the triangles cut out are isosceles with legs 20 feet long? 10. The bases of the Triangular Prism below have a total area of 36. If the two congruent lateral faces have a total area of 48, what is the height?

7 2006 Washington State Math Championship Unless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth. Geometry - Grade 8 1. The diagram shows an equiangular hexagon with side-lengths 12, 14, 18, 20, 22, 28 can be inscribed in an equilateral triangle with side-length 60. This same equiangular hexagon can also be inscribed in and equilateral triangle with side-length of n not equal to 60. What is the value on n In 1736, the cousin of the famous Gabriel Daniel Fahrenheit, Otto Fahrenheit, invented his angle measuring scale. No rotation was 32, and half a rotation was 212. When Otto Fahrenheit measured the angles of a hexagon with his not-sofamous Fahrenheit protractor and then added them what was the sum of the angles? 3. The net (2-d drawing of a 3-d shape) of a Greenhouse is given. The 20 by 20 square is the floor of the building. If the air system circulates 8 cubic feet per second, how many minutes will it take to circulate the entire volume of the building (answer to the nearest minute)? A isosceles right triangle is removed from each corner of a square piece of paper so that a rectangle remains (each big isosceles triangle has 9 times the area of the small isosceles triangle). What is the length of the rectangle longest side, if the sum of all 4 triangles is 200? 5. Steps are made first with frames and then cement is poured into the frames. You do not need to make bottoms on the frames. Below are the 2 ft dimensions of the frames. What is the cost of making the 6 in 6 in 4 ft 4 ft

8 steps given the prices below and if all boards must be one piece? Boards cost = $9 for 6 feet sections, 6 inches wide Cement cost = $6 for 4 cubic feet bags 6. Mr. Mo Lawnmower wants to cut out the grass triangular sections along the back of his house so he can plant some shrubs. However, feels bad about Fido (his dog) losing 120 ft some of his grass. Mr. Lawnmower vows to replace every square foot lost to the flowerbeds 60 ft 40 ft back onto the section of the very backyard. How x long will the new narrower section (40 ft wide) 20 ft'' become if the triangles cut out are isosceles with legs 20 feet long? 7. The bases of the Triangular Prism have a total area of 36. If the two congruent lateral faces have a total area of 48, what is the height? 8. Two pulleys with the same diameter of 20cm are 50cm apart. How long must the minimum length of the pulley be to reach around the pulleys (round to the nearest cm)? 50cm 20cm 20 cm 9. Find angle A in the diagram below. Hexagon is a regular hexagon. QDFX is a parallelogram. FAE is a isosceles triangle. H E Q D N X F A O G E 10. The area of a triangle is equal to.5x x+7.5. If the base is equal to (x+3), then what is the height in terms of x.

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