Download All answers on this test must be in simplest form (denominators

 All answers on this test must be in simplest form (denominators rationalized, expressions
simplified). Where applicable, leave solutions in terms of π.
March Regional
Geometry Team Question: 1
Let A = the 50th term of the sequence 9, 13, 17, 21, 25, 29…..
Let B = the number of diagonals in nonagon
Let C = the area of a regular hexagon with side length 12
Find
A B
C
All answers on this test must be in simplest form (denominators rationalized, expressions
simplified). Where applicable, leave solutions in terms of π.
March Regional
Let A = the 50th term of the sequence 9, 13, 17, 21, 25, 29…..
Let B = the number of diagonals in nonagon
Let C = the area of a regular hexagon with side length 12
Find
A B
C
Geometry Team Question: 1
March Regional
Geometry Team Question: 2
Let A = the ratio of the area of circle X to the area of circle Y if circle X has radius of
60
and
30
circle Y has circumference of 60π.
Let B = the ratio of the diagonals of square A to the diagonals of square B given square A
has side length 12 and square B with area = 256.
Let C = the ratio of the area of rhombus to the area of a hexagon when the rhombus has
side length of 10 and one diagonal length = 16 and the hexagon has a perimeter of 48.
Find
A B
C
March Regional
Geometry Team Question: 2
Let A = the ratio of the area of circle X to the area of circle Y if circle X has radius of
60
and
30
circle Y has circumference of 60π.
Let B = the ratio of the diagonals of square A to the diagonals of square B given square A
has side length 12 and square B with area = 256.
Let C = the ratio of the area of rhombus to the area of a hexagon when the rhombus has
side length of 10 and one diagonal length = 16 and the hexagon has a perimeter of 48.
Find
A B
C
March Regional
Geometry Team Question: 3
Express your answers in terms of π:
Let A = the area of a circle inscribed in an equilateral triangle with side length of 12 3 cm.
Let B = the circumference of a circle that circumscribes a regular hexagon with an area of 42 3
cm².
Let C = the length of a rectangle that has an area that is twice as large as its perimeter and a
width of 4.5 cm.
Let D = the length of the arc connecting two adjacent vertices of a regular pentagon inscribed in
A
 D
C
a circle of radius 7. Find:  
B
March Regional
Geometry Team Question: 3
Express your answers in terms of π:
Let A = the area of a circle inscribed in an equilateral triangle with side length of 12 3 cm.
Let B = the circumference of a circle that circumscribes a regular hexagon with an area of 42 3
cm².
Let C = the length of a rectangle that has an area that is twice as large as its perimeter and a
width of 4.5 cm.
Let D = the length of the arc connecting two adjacent vertices of a regular pentagon inscribed in
A
 D
C
a circle of radius 7. Find:   B
March Regional
Geometry Team Question: 4
If ABCD is a cyclic quadrilateral with side measures of 6, 7, 8 and 9, what is the area of the quadrilateral? March Regional
Geometry Team Question: 4
If ABCD is a cyclic quadrilateral with side measures of 6, 7, 8 and 9, what is the area of the quadrilateral? March Regional
Geometry Team Question: 5
Given the following sequences, find the smallest value of a1  25, a2  50, a3  75 ........
b1  1, b2  3, b3  6, b4  10 .........
March Regional
Geometry Team Question: 5
Given the following sequences, find the smallest value of a1  25, a2  50, a3  75 ........
b1  1, b2  3, b3  6, b4  10 .........
m
such that am  bn . n
m
such that am  bn . n
March Regional
Geometry Team Question: 6
. In order for Joe to calculate the heat loss of his architectural design, he needs to find the surface area that is exposed to the air. Arc ABC is a semicircle. All measurements are in feet. What is the surface area of Joe’s architectural design? March Regional
Geometry Team Question: 6
. In order for Joe to calculate the heat loss of his architectural design, he needs to find the surface area that is exposed to the air. Arc ABC is a semicircle. All measurements are in feet. What is the surface area of Joe’s architectural design? March Regional
Geometry Team Question: 7
Given circle O radius 6 and circle P radius 3, internal tangent ST and measure of angle ORS = 30°, find ST: T
3
R
O
P
30
6
S
March Regional
Geometry Team Question: 7
Given circle O radius 6 and circle P radius 3, internal tangent ST and measure of angle ORS = 30°, find ST: T
3
R
O
P
30
6
S
March Regional
Geometry Team Question: 8
8. The medians of triangle XYZ meet at point K with one vertex (X) located at the origin, vertex Y at (6q, 6r) and vertex Z at (6p, 0). What is the equation of median YN in slope intercept form when N is the point of intersection with side XZ? March Regional
Geometry Team Question: 8
8. The medians of triangle XYZ meet at point K with one vertex (X) located at the origin, vertex Y at (6q, 6r) and vertex Z at (6p, 0). What is the equation of median YN in slope intercept form when N is the point of intersection with side XZ? March Regional
Geometry Team Question: 9
Let A = the perimeter of parallelogram LMNP with LM  4, LN  8, PM  6 , Let B = the number of lines formed by 17 points in a plane, no 3 of which are collinear. Let C = the number of degrees in one point of a 12 pointed regular star. Let D = the area of a regular octagon inscribed in a circle with radius = 3 . Find BA
CD
March Regional
Geometry Team Question: 9
Let A = the perimeter of parallelogram LMNP with LM  4, LN  8, PM  6 , Let B = the number of lines formed by 17 points in a plane, no 3 of which are collinear. Let C = the number of degrees in one point of a 12 pointed regular star. Let D = the area of a regular octagon inscribed in a circle with radius = 3 . Find BA
CD
March Regional
Geometry Team Question: 10
A circle of radius 4 is inscribed in an equilateral triangle. The area inside the triangle and outside the circle = 3x   y . Find the value of x  y . March Regional
Geometry Team Question: 10
A circle of radius 4 is inscribed in an equilateral triangle. The area inside the triangle and outside the circle = 3x   y . Find the value of x  y . March Regional
Geometry Team Question: 11
Leave answers in terms of  . Let A = the area of an annulus formed by the inscribed and circumscribed circles of a regular hexagon side length = 9 Let B = the length of a diagonal of an isosceles trapezoid where side length l = 2 2 and
one base (b1 )  2 and one base (b2 )  4. Find: A  B
March Regional
Geometry Team Question: 11
Leave answers in terms of  . Let A = the area of an annulus formed by the inscribed and circumscribed circles of a regular hexagon side length = 9 Let B = the length of a diagonal of an isosceles trapezoid where side length l = 2 2 and
one base (b1 )  2 and one base (b2 )  4. Find: A  B
March Regional
Geometry Team Question: 12
1
th the 27
measure of one of its internal angles. How many sides does the polygon have?
The number of diagonals from a single vertex of a regular polygon is equal to March Regional
Geometry Team Question: 12
1
th the 27
measure of one of its internal angles. How many sides does the polygon have?
The number of diagonals from a single vertex of a regular polygon is equal to March Regional
Geometry Team Question: 13
Isosceles triangle ABC has mid‐segment MN and altitude AX. What is the ratio of the area of the shaded region to the area of the original triangle? A
M
B
N
C
X
March Regional
Geometry Team Question: 13
Isosceles triangle ABC has midsegment MN and altitude AX. What is the ratio of the area of the shaded region to the area of the original triangle? A
M
B
N
X
C
March Regional
Geometry Team Question: 14
A cylinder is cut on a slant as shown. The height on one side is reduced to 12. The radius of the base is 4. What is the volume of the cylinder?
March Regional
Geometry Team Question: 14
A cylinder is cut on a slant as shown. The height on one side is reduced to 12. The radius of the base is 4. What is the volume of the cylinder?
March Regional
Geometry Team Question: 15
Two circles are internally tangent at point G as indicated in the diagram below. If AB = 6, EF=8 and CD=6, find the sum of the radii of the two circles. Segment BD passes through the center of the larger circle. March Regional
Geometry Team Question: 15
Two circles are internally tangent at point G as indicated in the diagram below. If AB = 6, EF=8 and CD=6, find the sum of the radii of the two circles. Segment BD passes through the center of the larger circle.