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February Regional Geometry Team Question 1 Find A B C D A. B. C. D. The number of degrees in one angle in a regular polygon with 4 sides The number of degrees in one angle in a regular polygon with 8 sides The number of degrees in one angle in a regular polygon with 10 sides The number of degrees in one angle in a regular polygon with 20 sides February Regional Find Geometry Team Question 2 ABC in simplest form D A. B. C. D. Find the area of a isosceles trapezoid with height 1 and base lengths 4 and 6 Find the area of a regular hexagon with side length 6 The number of sides equal to one another in a equilateral triangle The number of degrees of an exterior angle in a decagon is D . Find D. February Regional Geometry Team Question 3 Kelly loves to group numbers based on similar patterns. Below is a table constructed by Kelly which she titled “Ordered Triplets.” Decipher the pattern and find A , where A is the product of all missing values B in columns 1&3 and B is the product of all the missing values in column 2. Column 1 12 15 9 24 6 13 12 45 12 Column 2 15 8 41 18 5 20 28 36 60 February Regional Find 9 A 5B 2C Column 3 9 40 30 10 12 53 37 45 61 Geometry Team Question 4 D in simplest form 5 A. The maximum number of diagonals that can be drawn within a regular hexagon B. Find the length of the shortest altitude in a 6, 8, 10 triangle C. If a rhombus has an area of 54 units 2 and a diagonal with length 12, find the length of the second diagonal D. A uniform border is constructed around a circular park with radius 1. If the area of the annulus formed is 24 , find the area of the entire region including the border. February Regional Find AC 8 BD Geometry Team Question 5 in simplest form A. The area of a triangle with side lengths 10, 10 and 12 81 3 8 C. The maximum number of diagonals that can be drawn within a pentagon D. The area of a circle with the equation x2 5x y 2 2 y 0 B. The perimeter of a hexagon with area February Regional Geometry Team Question 6 Find 2A B C in simplest form A. The area of a octagon with side length 4 4 x 8 3 C. The supplement of an angle is 4 times its complement. The supplement of the angle is D . B. The perimeter of the region bounded in the second quadrant by the equation y Find D February Regional Find Geometry Team Question 7 B 3 in simplest form A A. Find the geometric mean of 45 and 60 B. A car travels 45 miles at a constant speed before coming to a halt. Consider the wheels on the car to have a diameter of 10 yards. Find the total number of complete revolutions made by wheels of the car during this time. (1 mile ≈ 1760 yards) February Regional Geometry Team Question 8 Find A B 4 2 and an arc length of 25 5 4 2 B. Find the perimeter for a sector with an area of and an arc length of 25 5 A. Find the radius for a sector with an area of February Regional Find A Geometry Team Question 9 B in simplest form 2B C A. The circumference of a circle with radius r 3 B. The perimeter of a hexagon with side length 6 C. The area of a rhombus with diagonal lengths d1 8 and d 2 7 February Regional Geometry Team Question 10 Given CAB is formed by two tangents, CAB 60 , and the radius CD 6 ,find the area of BCD February Regional Geometry Team Question 11 Meghan and Richa are racing around a circular pool with diameter 40 meters. Both are to start from the same point, 20 meters from the pool, and race to a point (finish line) on the edge of the pool directly opposite of the start point. Meghan decides to run in a linear path directly to the pool at 5 m and then s m . Richa runs in a s m linear path, which forms a 30° angle with Meghan’s path, tangent to the pool at 2 3 and then runs s m around the edge of the pool at 4.8 . Who finishes first and what is the positive difference in the time s swims across in a linear path to the finish line on the other side of the pool at 1.6 (in seconds) that it takes both competitors to finish? February Regional Find Geometry Team Question 12 5BC AD A. The area of a rhombus with diagonal lengths of 12 and 6 B. The length of the diagonal in a isosceles trapezoid ABCD with side lengths AB 6 2 , BC 12 , CD 6 2 , and AD 24 C. The height of an equilateral triangle with area 9 3 D. The distance between the points 1, 2 and 4,6 February Regional Geometry Team Question 13 Find AB Let p m n and q r . A. Given B 60 , find A C D F B E G B. Consider a 45, 45,90 triangle. If a subsequent triangle is made by joining the mid-segments of the sides of the original triangle find the ratio of the area of the second triangle to the first triangle February Regional Geometry Team Question 14 Find the number of correct answers Simple geometric constructions use only these geometric instruments I. II. III. IV. Numbers A Compass A Straightedge A writing instrument February Regional Find Geometry Team Question 15 AB in simplest form CD A. B. C. D. Find the area of the kite Find the perimeter of the kite The numerical value of the sum of the angles in a kite The number of vertices that lie on a circle circumscribed about an anti-parallelogram (Hint: It’s a cyclic quadrilateral) 60° 12 90° 90° 120° 4 3