Download Find A B C D - + - ABC D

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