FGCU 2016 INVITATIONAL MATHEMATICS COMPETITION, GEOMETRY INDIVIDUAL. FGCU 2016 Invitational Mathematics Competition. Geometry Individual

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1 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) sq. yd B) 292 sq. yd C) sq. yd D) sq. yd E) NOTA 2) Find the length of the side marked x. A) 36 m B) 55 m C) 41 m D) 44 m E) NOTA 3) Name the polygon. A) hexagon B) octagon C) heptagon D) quadrilateral E) NOTA FGCU 2016 Invitational Mathematics Competition, Geometry Individual pg 1

2 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 pg 2

3 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 9) Find the area of the figure A) 30 sq. ft. B) 9 sq. ft. C) 15 sq. ft. D) 19.5 sq. ft. E) NOTA FGCU 2016 Invitational Mathematics Competition, Geometry Individual pg 3

4 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 Find the measure of the supplement of the angle 11) Find the supplement of 3 A) 357 B) 177 C)267 D) 87 E) NOTA 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 E) NOTA FGCU 2016 Invitational Mathematics Competition, Geometry Individual pg 4

5 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) m 1 = 50 ; m 2 = 130 ; m 3 = 50 B) m 1 = 40 ; m 2 = 130 ; m 3 = 40 C) m 1 = 130 ; m 2 = 40 ; m 3 = 130 D) m 1 = 130 ; m 2 = 50 ; m 3 = 130 E) 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 25- foot radius? A) 578 ft B) 34 ft C) 46 ft D) 17 ft E) NOTA FGCU 2016 Invitational Mathematics Competition, Geometry Individual pg 5

6 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 cm 3. 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) $ B) $ C) $ D) $ 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) $ B) $ 12, C) $ D) $ 15, E) NOTA 22) Find the measure of the complement of the angle ( )0. A) ( )0 B) ( )0 C) ( )0 D) 90 0 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 E) NOTA FGCU 2016 Invitational Mathematics Competition, Geometry Individual pg 6

7 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 28) Find the measure of the angle?. A) 40 B) 130 C) 50 D) 140 E) NOTA 29) The figure shows a regular polygon. Find the measure of angle 1. A) 135 B) 180 C) 108 D) 120 E) NOTA FGCU 2016 Invitational Mathematics Competition, Geometry Individual pg 7

8 30) A circle is inscribed in an equilateral triangle, the radius of the circle is 6 cm. Find the area of the triangle. F) B) 36 3 C) 72 3 D) E) NOTA FGCU 2016 Invitational Mathematics Competition, Geometry Individual pg 8