Download January Regional Geometry Team: Question #1 Points P, Q, R, S

January Regional
Points P, Q, R, S, and T lie in the plane with S on
and RT =
Geometry Team: Question #1
and R on
. If PQ = 5, PS = 3, PR = 5, QS = 3,
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
40 degrees.
that is defined by a central angle of
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
Let A = The area of a rectangle with sides of 4x + 4 and 3x + 6 and perimeter = 90
Let B = The measure of the diagonal of a square that has an area of 250
Let C = The perimeter of a rhombus with diagonals that measure 18 and 24
Let D = The measure of the 8th angle in an octagon when the average of the other 7 angles is 126°


Find  A 
D

CB
6

January Regional
Geometry Team: Question #8
A trapezoid has bases of length 10 and 15. Find the length of the segment that stretches from one leg of
the trapezoid to the other, parallel to the bases and passing through the point of intersection of the two
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
 AB   C 2
Find
1
D
10
January Regional
Given
Geometry Team: Question #10
l parallel to m find a + b + c + d
c
(not drawn to scale):
l
75
20
25
a
b
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
D
M
A
Consider this quadrilateral:
C
O
P
N
B
DM  MA
CN  NB
DC PB
mOPB = 90
DC = 68
AB = 44
BN = 15
DM = 12
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.