Geometry

a) Describe how to use composite figures to determine the area of a regular hexagon. b) Use your method to determine the area of a regular hexagon with side length 30 cm.

2. For the following triangle, write the full equation to solve for angle Q, and then solve for angle Q. [3]

Use the equation below to complete Parts I, II, and III. Part I: A parabola opens upward. The parabola goes through the point (3, -1), and the vertexis at (2, -2). What are the values of h and v? (2 point) Part II: To find the value of a, subtract the y-coordinate of the vertex from the y-coordinate ofthe point on the parabola that is 1 unit to the right of the vertex. Find the value of a for the parabola in Part I. Show your work. (3 points) Part IlI: Use Parts I and Il to write the equation of the parabola. (4 points)

7. Suppose a sphere has a volume of 3,000 cm³. Find the surface area. Part 1: Find the radius of the sphere by setting the volume equal to the formula above.Show your work and round the radius to the nearest hundredth. (5 points) Part II: Use the radius you found in Part I with the surface area formula below to the find-the surface area of the sphere. Show your work and round your answer to the nearest tenth. (5 points)

1.) Which shape seems to maximize the area of the protected region? 2.) Write down a generalization about the relationship between the area of a rectangle and its perimeter, when the perimeter remains constant. 3.) Perform similar calculations, but this time, use a constant area of 36 km?. Set up a table similar to the one above and calculate the perimeter of each configuration. 4.) Describe the rectangle that has the largest perimeter. Describe the rectangle that has the lowest perimeter. 5.) Write down a generalization about the relationship between the area of a rectangle and its perimeter, when the area remains constant. 6.) Give a real-life example of when you would use these generalizations, like the scenario given at the beginning of this investigation.

1. The following pairs are similar triangle with some dimensions specified. Find the measures of the other sides.

Xiao Jian wishes to use 6 identical square cards to form a cube net. He still has a square card which has not been assembled. Of the positions A, B and C, which cannot be assembled into the cube net? (A)A(B)B(C) C(D)all can

If a=3 and c=5, what is b? Enter irrational answers rounded to two decimal places.

3. Fill in the blanks with center, circle, directrix, focus, line, parabola, or radius. Ais the set of all points that are equidistant from two points. (1 point) A_________is the set of all points that are equidistant from a given point. The given pointis called the________The segment showing the distance is called the______.(3 A________is the set of all points equidistant from a single point and a single line. The single point is called the_______and the single line is called the________(3 points)

19 A straight road passes by a hill. The angle of elevation to the top of the hill is measured from three points A, B and C along the road. Point B is between points A and C such that AB = BC = 1200 m. The angle of elevation is 12.5° from point A and point B, and 9.5° from point C. Let h m be the height of the hill. Let Y be the top point of the hill and let X be the point vertically below Y at the same level as the road. a Find AX, BX and CX in terms of h.