Download Name - Westmount High School

1
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Parent Signature: _________________________________
Date: _________________________________
Grade 8 Test on Polygons
The badge chosen by a school committee is in the shape of a regular decagon.
a
HELLO
Write an equation to represent the perimeter p of the badge whose side measures a.
2
Construct a regular hexagon whose side measures 3 cm.
Show your work.
3
The adjacent figure is made up of congruent
isosceles trapezoids whose height is d. These
trapezoids form two regular octagons.
The shaded area between the two octagons
measures 1800 cm2.
The perimeter of the larger octagon is 200 cm.
One side of the smaller octagon measures 20 cm.
What is the distance d between the two octagons?
Show your work.
4
Paul’s father wants to install a pool in the shape of a regular hexagon. The sides of the pool will be
3 m long.
Draw the plan of the pool using the following scale : 1 cm equals 1.5 m.
5
The adjacent drawing represents the floor of the
new solarium in the Labrie home.
2m
The perimeter of the solarium, in the shape of a
regular hexagon, is 18 m.
In the centre of the solarium, there is a
rectangular ceramic decoration The width of the
rectangle is 1.5 m. The ratio between the width
and the length of the rectangle is 1:2.
Mr. Labrie wants to cover the rest of the floor
with a carpet that is sold at $24 a square metre,
all taxes included.
How much will the carpet cost?
Show your work.
9
0
2
3
5
2
7
6
1
8
4
3
1.5 m
0
9
6
The area of a regular polygon is 64.95 cm2. If the apothem is 4.33 cm and the sum of the interior
angles is 720, find the length of the sides of this polygon.
Show your work.
7
If all of the diagonals from one vertex of a polygon are drawn, four triangles are formed.
How many sides does this polygon have?
8
A)
8
C)
5
B)
6
D)
4
The perimeter of a regular octagon measures (24a  16) units.
Write an algebraic expression to represent the length of one side of the octagon.
9
Construct a regular pentagon with sides 3 cm in length.
10
Carla has a square garden, which has an area of 81 m5. Ben's garden is twice as long and twice as wide
as Carla's is.
What is the perimeter of Ben's garden?
Show your work.
11
You know that the sum of the measures of the interior angles of an 11-sided regular polygon is 1620.
Which formula allowed you to get the answer? Explain the formula (theorem).
12
In your answer booklet, construct a regular hexagon in a circle with a radius of 3 cm.
Explain your construction in your own words.
13
14
Which of the following statements is TRUE?
A)
A 5-sided regular polygon has only one axis of symmetry.
B)
A convex polygon can have an interior angle measuring more than 180.
C)
A 6-sided regular polygon can be divided into 6 equilateral triangles.
D)
The sum of the exterior angles of a 7-sided convex polygon is equal to 900.
Robert claims that the sum of the interior angles of a regular pentagon is 540.
On your answer sheet, complete the statement on which Robert based his claim.
15
Dario built a patio next to his circular
swimming pool with diameter 8 m, as shown
by the diagram on the right. He wants to cover
the patio with carpet that sells for $5.25 a
square metre. The length of each side of the
patio is equal to the length of the pool’s
diameter.
How much will it cost to carpet the patio, to the
nearest dollar?
8m
pool
patio
8m
8m
Show your work.
16
The area of a regular polygon is 43.44 cm2. Its apothem measures 3.62 cm.
When all diagonals that originate at the same vertex are drawn, the polygon is divided into 6 triangles.
What is the length of one side of this regular polygon?
Show your work.
17
The adjacent figure represents a section of tiled
pavement made up of regular polygons.
3 4
2 1
What is the measure of angle 4?
18
A)
42
C)
60
B)
45
D)
72
The sketch for a walking trail in a national park is shown on
the right. The heptagon is regular.
The architect did not provide the measures of the interior
angles of the figure.
Julie decides that she can find the measure of the interior
900
 128.6 .
angles using the following calculation:
7
What statement can be used to justify the use of 900 in this calculation?
19
A company’s logo is shown on the right.
The area of sector AOB is 75.36 cm2 and angle
AOB measures 60.
Each side of the regular hexagon measures14 cm.
What is the area of the black part of the logo?
Show all your work.
B
A
O
20
21
Which pair of figures below is necessarily similar?
A)
2 rhombuses
C)
2 rectangles
B)
2 triangles
D)
2 squares
All the diagonals from the same vertex of a regular polygon are drawn, forming 3 triangles. The area of
the polygon is 440 cm2 and its apothem measures 11 cm.
What is the length of one side of this regular polygon?
Show all your work.
22
The area of a stop sign, in the shape of a regular
octagon, is 5730 cm2 .The measure of its apothem is
41.6 cm.
What is the perimeter of the sign?
A)
137.74 cm
C)
2203.85 cm
B)
275.48 cm
D)
2844.20 cm
23
Given regular hexagons ABCDEF
and UVWXYZ.
A
B
The two figures are similar. The
measure of the sides of the large
hexagon is 2.5 times greater than the
measure of the sides of the small
hexagon.
U
V
8 cm
F
W
Z
In the small hexagon:
 the measure of side UV is 8 cm
 its apothem measures 7 cm
.
C
a = 7 cm
Y
X
D
E
What is the area of the shaded section between the two hexagons?
Show all your work.
24
For which regular polygon is the sum of the interior angles 1080°?
A)
Decagon
C)
Octagon
B)
Hexagon
D)
Pentagon
25
In your Answer Booklet, construct a regular octagon having each side measure 3 cm.
26
At Romeo and Juliette's wedding reception, lace will be placed along the edges of the top of the gift
table. The tabletop is a regular hexagon. The area of the hexagon is 17 466 cm2 and its apothem
measures 71 cm. The lace costs $3.20 per metre.
What will be the total cost of the lace?
Show all your work.
27
28
Which of the following statements is TRUE?
A)
A regular hexagon has only one line of symmetry.
B)
The sum of the interior angles of a regular pentagon is 540.
C)
The sum of the exterior angles of a regular polygon is 180.
D)
The diagonals drawn from a vertex of a 10-sided polygon divide the polygon into
5 triangles.
The area of the equilateral triangle on the right is 15.6 cm2.
Its height is 5.2 cm.
5.2 cm
What is the perimeter of this equilateral triangle?
29
A picture frame is in the shape of a regular octagon with side 8.3 cm.
The artist who designed the frame would like to design another one in the shape of a regular pentagon,
but with the same perimeter as the original.
What is the length of one side of this new frame?
30
A)
5.19 cm
C)
13.28 cm
B)
9.96 cm
D)
41.50 cm
Ramona's pet rabbits play in a yard shaped like a regular
hexagon.
Fences separate the rabbits and surround each of the six pens, as
shown.
Apothem = 4.68 m
2
The total area of the yard is 75.8 m .
How many metres of fencing are required to build all six pens? (to the nearest metre)
Show all your work.
31
The perimeter of a regular hexagon is (30x + 6) units.
What is the simplified algebraic expression that corresponds to the length of one of its sides?
32
A circular pool with a fountain in the centre has been
installed in a town park.
A fence in the form of a regular hexagon is constructed
so that the pool touches each side of the hexagon, as
shown in the diagram on the right.
Fountain
The pool has a diameter of 26 m.
The length of each side of the regular hexagon is 15 m.
The town wants to plant grass in the areas that are
shaded in the diagram.
The cost of the grass is $4.25/m2.
Excluding taxes, what will it cost the town to plant the grass around the pool?
Show your work.
15 m
33
A hotel has a deck on its property.
The deck was formed by constructing 4 regular pentagons around a square area, as shown in the
diagram below.
The outside perimeter of the deck is 139.2 m.
The area of the deck is 597.69 m2.
Beams
A building inspector told the hotel owners that 2 beams must be installed under the deck for more
support.
These beams are to run from the centre of one regular pentagon to the centre of the opposite regular
pentagon.
How long is each beam?
Show your work.
34
The floor area of a room has the shape of a regular pentagon, as shown below.
Its area is 440 m2 and its apothem is 11 m.
?
11 m
What is the length of one side of the floor?
Area : 440 m2
35
0.45 km
The City of Châteauguay has just built a new park.
Its shape and dimensions are shown in the diagram.
Ms. Anderson mows the grass for all Châteauguay
parks.
0.8 km
It takes her 2 hours to mow an area of 1.5 km2.
How long will it take her to mow the grass at this new park?
Show your work. (Round your final answer to the nearest tenth of an hour.)
36
Two regular hexagons that are attached along one side, as shown below, have centers at A and B.
The length of segment AB is 10.4 m.
The area of each hexagon is 93.6 m2.
What is the length of any one side?
Show all your work.
A
10.4 m
B
37
Mr. Leo has a circular garden. He wanted to set aside a sector of the circular garden for his roses.
Mr. Leo measured a central angle of 120 to create this sector.
The arc length of the sector is 37.68 m.
What is the area of the sector in which Mr. Leo planted his
roses?
Round your answer to the nearest square metre.
37.68 m
roses
120
Show all your work.