January Regional Geometry Team: Question #1 Points P, Q, R, S, and T lie in the plane with S on and R on. If PQ = 5, PS = 3, PR = 5, QS = 3, and RT = 4, what is ST? 3 January Regional Geometry Team: Question #2 The perimeter of a regular hexagon is 24 meters. What is the area of the hexagon?
January Regional Geometry Team: Question #3 Below are 6 statements. Each statement is assigned a value. Add up the values of each of the false statements. (-4) A polygon with 40 sides has 720 diagonals (2) The area of a trapezoid is equal to the product of its height and the length of its mid-segment (4) Every square is a rhombus (6) The measure of an external angle on a regular heptagon is 90 degrees (3) If the lengths of the sides of a triangle are 50 cm, 120 cm and 130 cm, then the triangle is a right triangle. (-5) If the volumes of two similar polygons are in the ratio of 16³ to 49³ then their corresponding surface areas are in the ratio 4² to 7². January Regional Geometry Team: Question #4 A regular polygon of side length 1 has the property that if regular pentagons of side length 1 are placed on each side, then each pentagon shares a side with two adjacent ones. How many sides does such a polygon have?
January Regional Geometry Team: Question #5 Let X = the sum of the measures of the external angles of a 20-gon. Let Y = the number of sides of a regular polygon that has interior angle measures of 168 degrees. Let Z = the number of sides of a regular polygon that has exterior angle measures of 18 degrees. Let A = the number of letters in the point of concurrency defined by the intersection of the altitudes of a triangle. Find A(X) Z(Y) January Regional Geometry Team: Question #6 Let A = The exact measure of the acute angle formed by the hands of a clock at 3:20. Let B = The radius of a circle that has a sector having an area 9 that is defined by a central angle of 40 degrees. Let C = The number of regions into which a plane is divided when 12 parallel lines are drawn in the plane. Let D = The volume of a hemisphere with a radius of 3. Find A + B + C + D.
January Regional Geometry Team: Question #7 LetA=Theareaofarectanglewithsidesof4x+4and3x+6andperimeter=90 LetB=Themeasureofthediagonalofasquarethathasanareaof250 LetC=Theperimeterofarhombuswithdiagonalsthatmeasure18and24 LetD=Themeasureofthe8 th angleinanoctagonwhentheaverageoftheother7anglesis126 Find! D $ A + # C " % B & 6 ' January Regional Geometry Team: Question #8 Atrapezoidhasbasesoflength10and15.Findthelengthofthesegmentthatstretchesfromonelegof thetrapezoidtotheother,paralleltothebasesandpassingthroughthepointofintersectionofthetwo diagonals.
January Regional Geometry Team: Question #9 Let A = The sum of two exterior angles of an icosagon Let B = The number of sides that a hendecagon has Let C = The number of diagonals in a heptagon Let D = The number of interior angles in a hectagon Find 2 ( AB)! C 1 10 D January Regional Geometry Team: Question #10 Given l parallel to m find a + b + c + d (not drawn to scale): a 20 b c 75 l 15 85 d 85 m
January Regional Geometry Team: Question #11 Let D = The distance between two points, (-3, 7) and (-12, 3). Let H = The length of the hypotenuse in a right triangle with leg measures of 4 and 5. Let S = The area of a 135 sector in a circle with area 32π ft². Let A = The surface area of a cube with a side length of 5. Arrange the answers in descending order. January Regional Geometry Team: Question #12 Equilateral triangle ABC has side length of 24. Points D, E and F lie on sides BC, CA and AB such that AD is perpendicular to BC, DE is perpendicular to AC and EF is perpendicular to AB. G is the intersection of AD and EF. Find the area of quadrilateral BFGD.
January Regional Geometry Team: Question #13 Upon cutting a certain rectangle in half, you obtain two rectangles that are scaled down versions of the original. What is the ratio of the longer side length to the shorter side length January Regional Geometry Team: Question #14 In the diagram below, the outer circle has a radius of 3 and the inner circle has a radius of 2. What is the area of the shaded region?
January Regional Geometry Team: Question #15 N P B Consider this quadrilateral: Let S = MN Let T = MP Let U = The Perimeter of ABCD Let V = The measure of angle DON Find: S + T + U V Express your answer as an improper fraction.