C Challenge

42. Proof Prove that the bisectors of the angles of a regular polygon are concurrent and that they are, in fact, radii of the polygon. (Hint: For regular n-gon ABCDE …, let P be the intersection of the bisectors of ∠ A B C angle eh b c  and ∠ B C D . angle b c d .  Show that D P ¯ d p bar  must be the bisector of ∠ C D E . ) angle c d e . close
43. Coordinate Geometry A regular octagon with center at the origin and radius 4 is graphed in the coordinate plane.
    1. Since V 2 v sub 2  lies on the line y = x , y equals x comma  its x- and y-coordinates are equal. Use the Distance Formula to find the coordinates of V 2 v sub 2  to the nearest tenth.
    2. Use the coordinates of V 2 v sub 2  and the formula A = 1 2 b h eh equals . 1 half , b h  to find the area of Δ V 1 O V 2 cap delta , v sub 1 . o , v sub 2  to the nearest tenth.
    3. Use your answer to part (b) to find the area of the octagon to the nearest whole number.

       

Standardized Test Prep

SAT/ACT

44. What is the area of a regular pentagon with an apothem of 25.1 mm and perimeter of 182 mm?
    1. 913 . 6   m   m 2 913 . 6 m , m squared
    2. 2284 . 1   m   m 2 2284 , . 1 m , m squared
    3. 3654 . 6   m   m 2 3654 , . 6 m , m squared
    4. 4568 . 2   m   m 2 4568 , . 2 m , m squared
45. What is the most precise name for a regular polygon with four right angles?
    6. square
    7. parallelogram
    8. trapezoid
    9. rectangle
46. Δ A B C cap delta eh b c  has coordinates A ( − 2 , eh open negative 2 comma  4), B(3, 1), and C ( 0 , − 2 ) . c open 0 comma negative 2 close .  If you reflect Δ A B C cap delta eh b c  across the x-axis, what are the coordinates of the vertices of the image Δ A ′ B ′ C ′ ? cap delta eh , prime b . prime c prime question mark
    1. A ′ ( 2 ,   4 ) , B ′ ( − 3 , 1 ) , C ′ ( 0 , − 2 ) eh prime open 2 comma 4 close comma b prime open negative 3 comma . 1 close comma c prime open 0 comma negative 2 close
    2. A ′ ( − 2 , − 4 ) , B ′ ( 3 , − 1 ) , C ′ ( 0 , 2 ) eh prime open negative 2 comma . negative 4 close comma b prime . open 3 comma negative 1 close comma c prime open 0 comma 2 close
    3. A ′ ( 4 , − 2 ) , B ′ ( 1 ,   3 ) , C ′ ( − 2 , 0 ) eh prime open 4 comma negative 2 close comma b prime . open 1 comma 3 close comma c prime open negative 2 comma 0 close
    4. A ′ ( 4 ,   2 ) , B ′ ( 1 , − 3 ) , C ′ ( − 2 , 0 ) eh prime open 4 comma 2 close comma b prime open 1 comma negative 3 close comma c prime . open negative 2 comma 0 close

Short Response

47. An equilateral triangle on a coordinate grid has vertices at (0, 0) and (4, 0). What are the possible locations of the third vertex?

Mixed Review

See Lesson 10-2.

48. What is the area of a kite with diagonals 8 m and 11.5 m?

49. The area of a trapezoid is 42   m 2 . 42 , m squared , .  The trapezoid has a height of 7 m and one base of 4 m. What is the length of the other base?

Get Ready! To prepare for Lesson 10-4, do Exercises 50–52.

See Lesson 1-8.

Find the perimeter and area of each figure.

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