Download fgcu 2016 invitational mathematics competition, geometry individual

FGCU 2016 INVITATIONAL MATHEMATICS COMPETITION, GEOMETRY INDIVIDUAL
FGCU 2016 Invitational Mathematics Competition
Geometry Individual
Name: ________________________________________
School/Team: ________________________________________
MULTIPLE CHOICE: Choose the one alternative that best completes the statement or answers the
question.
1) Find the area of the figure.
A) 481.8 sq. yd
B) 292 sq. yd
C) 240.9 sq. yd
D) 189.8 sq. yd
E) NOTA
C) 41 m
D) 44 m
E) NOTA
C) heptagon
D) quadrilateral
E) NOTA
2) Find the length of the side marked x.
A) 36 m
B) 55 m
3) Name the polygon.
A) hexagon
B) octagon
FGCU 2016 Invitational Mathematics Competition, Geometry Individual
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FGCU 2016 INVITATIONAL MATHEMATICS COMPETITION, GEOMETRY INDIVIDUAL
4) Classify the angle as acute, right, straight, obtuse or NOTA
A) acute
B) straight
C) obtuse
D) right
E) NOTA
5) Find the perimeter of the figure named and shown. Express the perimeter in the same unit of
measure that appears on the given side or sides.
Rectangle
A) 30 mi
B) 12 mi
C) 18 mi
D) 15 mi
E) NOTA
6) Use the appropriate inverse trigonometric function on a calculator to find the measure of angle
A, rounded to the nearest whole degree.
A) 33°
B) 31°
C) 32°
D) 34°
E) NOTA
FGCU 2016 Invitational Mathematics Competition, Geometry Individual
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FGCU 2016 INVITATIONAL MATHEMATICS COMPETITION, GEOMETRY INDIVIDUAL
Solve the problem.
7) For one instant, a hot air balloon is 500 feet above the ocean. The figure shows that the angle of
depression from the balloon to point P is 32°. How far, to the nearest foot, is point P to the point
directly below the balloon on the surface of the water?
A) 339 feet
B) 800 feet
C) 196 feet
D) 259 feet
E) NOTA
8) Find the measure of the angle A for the triangle shown.
A) 90°
B) 88°
C) 78°
D) 168°
E) NOTA
C) 15 sq. ft.
D) 19.5 sq. ft.
E) NOTA
9) Find the area of the figure
A) 30 sq. ft.
B) 9 sq. ft.
FGCU 2016 Invitational Mathematics Competition, Geometry Individual
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FGCU 2016 INVITATIONAL MATHEMATICS COMPETITION, GEOMETRY INDIVIDUAL
10) Use the Pythagorean Theorem to find the missing length in the right triangle. Use a calculator to
find square roots, rounding, if necessary, to the nearest tenth
A) 9 mi
B) 7 mi
C) 10 mi
D) 8 mi
E) NOTA
D) 87°
E) NOTA
Find the measure of the supplement of the angle
11) Find the supplement of 3°
A) 357°
B) 177°
C)267°
12) Find the measures of the parts of the right triangle that are not given.
Round your answers to the nearest whole number.
A) a = 33 yd; c = 66 yd; ∠ B = 60°
B) a = 37 yd; c = 64 yd; ∠ B = 60°
C) a = 33 yd; c = 64 yd; ∠ B = 60°
D) a = 37 yd; c = 66 yd; ∠ B = 60°
E) NOTA
13) Find the perimeter of the figure named and shown. Express the perimeter in the same unit of
measure that appears on the given side or sides.
Equilateral triangle
A) 288 mi
B) 71 mi
C) 72 mi
D) 48 mi
FGCU 2016 Invitational Mathematics Competition, Geometry Individual
E) NOTA
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FGCU 2016 INVITATIONAL MATHEMATICS COMPETITION, GEOMETRY INDIVIDUAL
Use the Pythagorean Theorem to solve the problem. Use your calculator to find square roots,
rounding, if necessary, to the nearest tenth.
14) A square sheet of paper measures 28 centimeters on each side. What is the length of the
diagonal of this paper?
A) 1568 cm
B) 56 cm
C) 28 cm
D) 39.6 cm
E) NOTA
15) A garden is in the shape of a rectangle 27 feet long and 14 feet wide. If fencing costs $8 a foot,
what will it cost to place fencing around the garden?
A) $656
B) $1312
C) $3024
D) $328
E) NOTA
16) Find the measures of angles 1, 2, and 3.
A)
B)
C)
D)
E)
m∠ 1 = 50°; m∠ 2 = 130 °; m ∠ 3 = 50°
m∠ 1 = 40°; m ∠ 2 = 130 °; m∠ 3 = 40°
m∠ 1 = 130°; m ∠ 2 = 40 °; m ∠ 3 = 130°
m∠ 1 = 130°; m ∠ 2 = 50 °; m ∠ 3 = 130°
NOTA
17) Find the perimeter of the figure named as shown. Express the perimeter in the same unit of
measure that appears on the given side or sides.
Parallelogram
A) 471 flowers
B) 158 flowers
C) 314 flowers
D) 942 flowers
E) NOTA
Solve the problem. Round all circumference and area calculations to the nearest whole number.
18) How many flowers spaced every 6 inches are needed to surround a circular garden with a 25foot radius?
A) 578 ft
B) 34 ft
C) 46 ft
D) 17 ft
FGCU 2016 Invitational Mathematics Competition, Geometry Individual
E) NOTA
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FGCU 2016 INVITATIONAL MATHEMATICS COMPETITION, GEOMETRY INDIVIDUAL
19) A 15-foot pole is supported by two wires that extend from the top of the pole to points that are
each 8 feet from the base of the pole. Find the total length of the two wires.
A) 578 ft
B) 34 ft
C) 46 ft
D) 17 ft
E) NOTA
20) A special stainless-steel cone sits on top of a cable television antenna. The cost of the stainless
steel is $7.00 per 𝑐𝑚3 . The cone has a radius of 4 cm and a height of 10 cm. What is the cost of
the stainless steel needed to make this solid steel cone? Round to the nearest cent.
A) $1172.86
B) $586.43
C) $373.33
D) $293.22
E) NOTA
21) A parking area that is to be resurfaced is shaped like a trapezoid. The bases are 80 feet and 110
feet, and the height is 60 feet. What is the cost if the price of the resurfacing is $1.40 per square
foot?
A)
$
7980.00
B) $12,320.00
C) $5700.00
D) $15, 960.00
E) NOTA
1 0
22) Find the measure of the complement of the angle (43 3) .
2 0
A) (136 3)
2 0
B) (47 3)
2 0
C) (46 3)
D) 900
E) NOTA
23) Find the sum of the measures of the angles of a hexagon
A) 540°
B) 1080 °
C) 720°
D) 180°
E) NOTA
24) The rectangular front of a house measures 27 feet by 33 feet. A rectangular door on the side of
the house measures 7 feet by 4 feet. There are also 9 rectangular windows on the front of the
house, each measuring 4 feet by 3 feet. How many square feet of siding will be needed to cover
the front of the house not counting the area covered by the door and windows?
A) 851 𝑓𝑡 2
B) 755 𝑓𝑡 2
C) 136 𝑓𝑡 2
D) 891 𝑓𝑡 2
E) NOTA
25) A flagpole casts a shadow of 24 feet. Nearby, a 7-foot tree casts a shadow of 3 feet. What is the
height of the flag pole?
A) 56 ft.
B) 10.3 ft
C) 504 ft.
D) 0.9 ft
FGCU 2016 Invitational Mathematics Competition, Geometry Individual
E) NOTA
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FGCU 2016 INVITATIONAL MATHEMATICS COMPETITION, GEOMETRY INDIVIDUAL
26) Find the measure of the angle ?° .
A) 60°
B) 155°
C) 120 °
D) 65°
E) NOTA
27) Name the polygon
A) hexagon
B) pentagon
C) quadrilateral
D) heptagon
E) NOTA
C) 50°
D) 140 °
E) NOTA
28) Find the measure of the angle ?° .
A) 40 °
B) 130°
29) The figure shows a regular polygon. Find the measure of angle 1.
A) 135 °
B) 180 °
C) 108°
D) 120 °
FGCU 2016 Invitational Mathematics Competition, Geometry Individual
E) NOTA
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FGCU 2016 INVITATIONAL MATHEMATICS COMPETITION, GEOMETRY INDIVIDUAL
30) A circle is inscribed in an equilateral triangle, the radius of the circle is 6 cm. Find the area of the
triangle.
F) 109√3
B) 36√3
C) 72√3
D) 108√3
FGCU 2016 Invitational Mathematics Competition, Geometry Individual
E) NOTA
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