2012 Florida Mu Alpha Theta State Convention
THETA QUADRILATERALS
For all questions, “E) NOTA” means none of the above answers are correct.
Figures are not drawn to scale.
1. Jimmy owns a rectangular pool which measures 10 feet by 30 feet. He surrounds the pool with a
poured concrete deck that reaches exactly 3 feet from the pool at all points. What is the area of
the deck in square feet?
A)
B)
C)
2. A square has a perimeter of
square’s diagonals?
A) √
B)
√
D) 240
E)NOTA
This same square has an area of
C) √
D)
. How long is one of this
E)NOTA
3. Which of the following statements is false?
I. All squares are rhombi.
II. All rectangles are parallelograms.
III. All trapezoids are parallelograms.
A) II only
B) I and III
C) II and III
D) III only
E)NOTA
For questions 4-6, use the information in the box below:
Let CAMO be a rhombus with diagonals of length 6 and 12.
4. What is the perimeter of rhombus
A) √
B) √
C)
√
D)
√
E)NOTA
5. What is the area of rhombus
A) 18
B) 36
C) 54
D) 72
6. How many lines of symmetry does rhombus
A) 0
B) 1
C) 2
E)NOTA
have?
D) 4
E)NOTA
7. Which of the following would NOT prove that a quadrilateral is a parallelogram?
A) The diagonals bisect each other.
B) One pair of opposite sides is parallel and congruent.
C) Both pairs of opposite sides are congruent.
D) Both pairs of opposite angles are congruent.
E) NOTA
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2012 Florida Mu Alpha Theta State Convention
THETA QUADRILATERALS
8. A quadrilateral has degree measures of its interior angles in the ratio of 1:3:6:8. What is the
degree measure of the smallest exterior angle?
A)
B)
C)
9. Given rhombus MIKE, ∠M
be a possible angle measure for ∠E?
A)
B)
D)
E)NOTA
and ∠K
C)
D)
. Which of the following could
E)NOTA
10. Quadrilateral DWIG is similar to quadrilateral SHRU. DWIG has an area of 10, and DW has a
length of 3. If SH has a length of 7, what is the area of quadrilateral SHRU ?
A)
B)
C)
D)
E)NOTA
11. A square and a rectangle have equal areas. The length of a diagonal of the square is √ . If the
ratio of the width to the length of the rectangle is 1:9, what is the perimeter of the rectangle?
A)
√
B)
C) 50
D)
E)NOTA
12. How many 4-centimeter by 4-centimeter floor tiles would it take to completely tile the floor of a
40-meter by 15-meter cafeteria?
A) 125,000
B) 375,000
C) 480,000
13. In parallelogram ZEUS,
A)
D)
D) 750,000
E)NOTA
. What is the measure of ∠E?
B)
E) NOTA
C)
14. If the width of a rectangle is increased by 80%, by what percentage must the length be
decreased if the area is to remain the same?
A)
B) 20%
C) 25%
D) 80%
E) NOTA
15. What is the sum of all of the exterior angles of a parallelogram? (An exterior angle is defined as
the angle between the side of the parallelogram and its adjacent side extension.)
A) 90
B) 180
C) 270
D) 360
2
E) NOTA
2012 Florida Mu Alpha Theta State Convention
THETA QUADRILATERALS
16. Jenny has just purchased a rectangular painting that is mounted on a circular plate. This
perimeter of this circular plate circumscribes the rectangular painting. She has decided that the
painting, mounted on the plate, would look better framed by a circular wooden frame that has a
width of 4 inches. The painting has a height of 10 inches and a length of 24 inches. Ed’s Frame
Shop charges $4 per square foot of wood in the frame. How much will the frame cost?
A)
B)
C)
D)
E)NOTA
17. Buster is building a game room and purchases a square
dartboard, shown in the figure to the right. If x = 2 inches,
what is the probability of a dart landing in the shaded
region?
A)
B)
C)
D)
E)NOTA
18. At Jeanine’s Textbook Company, she sells only one size of cardboard boxes for shipping
textbooks. One face of the box has an area of 45 in2. Another face of the same box has an area of
72 in2. The volume of the box is 1080 in3. If cardboard is $1.00 per square foot, how much will
the company spend on cardboard producing one box, to the nearest dollar? Assume the
cardboard has negligible thickness.
A)
B) $5.00
C) $6.00
D) $7.00
E)NOTA
19. Find the area of quadrilateral PERU if PE=7, ER=3, RU=6, UP=6, and ∠P is supplementary to ∠R.
A)
√
B)
√
C)
√
D) Cannot be determined.
E)NOTA
20. Rhombus SOFT has sides of length 5. What is the area of rhombus SOFT ?
A) 25
B)
√
C)
D) Cannot be determined.
21. In the figure to the right, quadrilateral FROG contains an
inscribed circle. If FROG has a perimeter of 14 and an area of
√ , then what is the area of the inscribed circle?
A)
B)
D)
E)NOTA
C)
3
E)NOTA
2012 Florida Mu Alpha Theta State Convention
THETA QUADRILATERALS
22. Which of the following is the definition of a bicentric quadrilateral?
A) A quadrilateral with exactly two lines of symmetry.
B) A quadrilateral which has an incircle and a circumcircle.
C) A quadrilateral with diagonals of equal length.
D) A quadrilateral that can be constructed using only two congruent triangles.
E) NOTA
For questions 23 and 24, use the information in the box below:
Let
(
be a quadrilateral on the Cartesian plane with points at J(
)
23. Which of the following describe quadrilateral
)
(
)
(
)
?
A) trapezoid
B) rhombus
C) rectangle
D) kite
E) NOTA
24. What is the area of quadrilateral
A) 6
B) √
C) √
?
D) 7
E) NOTA
25. Hexagon ABCDEF, pictured to the right, is a regular
hexagon. Four vertices are randomly chosen and
connected to form a quadrilateral. When this
quadrilateral is named clockwise, the vertices are in
alphabetical order. What is the probability that the four
joined vertices will form an isosceles trapezoid?
A)
B)
D)
E)NOTA
C)
26. A rectangle is 4 times as long as it is wide, measured in inches. If the length is increased by 4
inches and the width is decreased by 1 inch, the area will be 60 square inches. What was the
area of the original rectangle, in square inches?
A) 48
B) 60
C) 64
D) 68
E) NOTA
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2012 Florida Mu Alpha Theta State Convention
THETA QUADRILATERALS
(
)
27. A parabola has an equation of
Points A and B represent the intersection of
the parabola’s latus rectum with the parabola.
and
run through points A and B
respectively. Find the area of the rectangle bounded by
the latus rectum, and the
directrix.
A) 36
B) 18
C) 9
D) 4.5
E) NOTA
For questions 28-30 use the information in the box below:
Quadrilateral YETI has an interior that is defined as the bound area of the following equations:
| |
| |
28. Which of the following describe quadrilateral YETI ?
A) kite
B) rhombus
C) rectangle
D) trapezoid
E) NOTA
29. Find the perimeter of quadrilateral YETI.
A) √
D) √
B) √
√
E) NOTA
C) √
√
30. Find the volume of the solid generated when quadrilateral YETI is rotated around the y-axis.
A)
B)
C)
D)
5
E) NOTA