Rectilinear Figures

Rectilinear Figures, SM-Bank 045

An isosceles triangle has a base of length 4 centimetres and a perimeter of 20 centimetres.

Find the length of the equal sides. (2 marks)

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$8\ \text{cm}$

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$\text{Let the length of the equal sides be}\ x$

$\text{Then,}\ \ 2\times x+4$	$=20$
$2x$	$=20-4$
$2x$	$=16$
$x$	$=8$

$\therefore\ \text{The equal sides are of length }8\ \text{cm}$

Rectilinear Figures, SM-Bank 044

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Find the perimeter of the following irregular shape. (2 marks)

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$70\ \text{mm}$

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$\text{Perimeter}$

$=7+13+20+9+6+15$

$=70\ \text{mm}$

Rectilinear Figures, SM-Bank 043

Find the perimeter of the following irregular shape. (2 marks)

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$38\ \text{cm}$

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$\text{Perimeter}$

$=10+5+3+4+7+9$

$=38\ \text{cm}$

Rectilinear Figures, SM-Bank 042

Find the perimeter of the following irregular shape. (2 marks)

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$38.8\ \text{m}$

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$\text{Perimeter}$

$=10.2+2\times 3.1 +4\times 2.4+4\times 1.8+5.6$

$=38.8\ \text{m}$

Rectilinear Figures, SM-Bank 041

Mark all missing lengths on the following shape. (1 mark)

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Calculate the perimeter. (2 marks)

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b. $390\ \text{m}$

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b. $\text{Perimeter}$

$=87+5\times 32+44+99$

$=390\ \text{m}$

Rectilinear Figures, SM-Bank 040

Mark all missing lengths on the following shape. (1 mark)

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Calculate the perimeter. (2 marks)

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b. $54\ \text{mm}$

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b. $\text{Perimeter}$

$=13+2\times 9+4+2\times 5+3+6$

$=54\ \text{mm}$

Rectilinear Figures, SM-Bank 039

Mark all missing lengths on the following shape. (1 mark)

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Calculate the perimeter. (2 marks)

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b. $52\ \text{cm}$

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b. $\text{Perimeter}$

$=12+14+5+10+7+4$

$=52\ \text{cm}$

Rectilinear Figures, SM-Bank 038

Calculate the perimeter of the following polygon. (2 marks)

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$6\ \text{m}$

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$\text{Perimeter}$

$=5\times 1.2$

$=6\ \text{m}$

Rectilinear Figures, SM-Bank 037

Calculate the perimeter of the following trapezium. (2 marks)

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$28.8\ \text{mm}$

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$\text{Perimeter}$

$=6+7.2+4.8+10.8$

$=28.8\ \text{mm}$

Rectilinear Figures, SM-Bank 036

Calculate the perimeter of the following kite. (2 marks)

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$34.2\ \text{cm}$

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$\text{Perimeter}$

$=2\times 12.3+2\times 4.8$

$=34.2\ \text{cm}$

Rectilinear Figures, SM-Bank 035

Calculate the perimeter of the following parallelogram. (2 marks)

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$228\ \text{cm}$

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$\text{Perimeter}$

$=2\times 73+2\times 41$

$=228\ \text{cm}$

Rectilinear Figures, SM-Bank 034

Calculate the perimeter of the following triangle. (2 marks)

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$38.8\ \text{m}$

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$\text{Perimeter}$

$=15.3+12+11.5$

$=38.8\ \text{m}$

Rectilinear Figures, SM-Bank 033

Calculate the perimeter of the following triangle. (2 marks)

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$15.3\ \text{mm}$

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$\text{Perimeter}$

$=3\times 5.1$

$=15.3\ \text{mm}$

Rectilinear Figures, SM-Bank 032

Calculate the perimeter of the following triangle. (2 marks)

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$51\ \text{cm}$

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$\text{Perimeter}$

$=2\times 19+13$

$=51\ \text{cm}$

Rectilinear Figures, SM-Bank 031

Calculate the perimeter of the following rhombus. (2 marks)

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$64\ \text{cm}$

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$\text{Perimeter}$

$=4\times 16$

$=64\ \text{cm}$

Rectilinear Figures, SM-Bank 030

Calculate the perimeter of the following square. (2 marks)

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$42\ \text{m}$

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$\text{Perimeter}$

$=4\times 10.5$

$=42\ \text{m}$

Rectilinear Figures, SM-Bank 029

Calculate the perimeter of the following rectangle. (2 marks)

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$366\ \text{mm}$

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$\text{Perimeter}$

$=2\times 36 +2\times 147$

$=366\ \text{mm}$

Rectilinear Figures, SM-Bank 028

Calculate the perimeter of the following rectangle. (2 marks)

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$35.8\ \text{cm}$

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$\text{Perimeter}$

$=2\times 12.3 +2\times 5.6$

$=35.8\ \text{cm}$

Rectilinear Figures, SM-Bank 027

A farmer uses the river bordering his property and fencing to create a large grazing paddock for his horses, as shown in the diagram below.

The fencing has 4-strand wiring which is also shown below.

Given that fencing is not required on the river boundary, how many kilometres of wire will be required to fence the rest of the paddock? (2 marks)

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$5.6\ \text{km}$

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$\text{Wire needed}$

$=4\times(700+200+300+1100+200+200+1200)$

$=4\times 3900$

$=15\ 600\ \text{m}=15.6\ \text{km}$

Rectilinear Figures, SM-Bank 026

Jill cut a piece of binding in half.

She then placed one half on top of the other half, as shown below.

What is the perimeter of the newly formed shape in millimetres? (2 marks)

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$1600\ \text{mm}$

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$\text{Calculating the perimeter clockwise from top right:}$

$\text{Perimeter}$

$=18+2\times 382 +18+2\times 400$

$=1600\ \text{mm}$

Rectilinear Figures, SM-Bank 025

Martha cut a piece of material in half as shown below.

She then placed the one half on top of the other half, as shown below.

What is the perimeter of the newly formed shape in millimetres? (2 marks)

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$320\ \text{mm}$

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$\text{Calculating the perimeter from the top down:}$

$\text{Perimeter}$

$=30+2\times 50+2\times 25+2\times 30+80$

$=320\ \text{mm}$

Rectilinear Figures, SM-Bank 024

A rectangle has a length of 12 cm and a width of 7 cm.

A square has the same perimeter as this rectangle.

What is the side length of this square in centimetres? (2 marks)

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$9.5\ \text{cm}$

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$\text{Perimeter of Rectangle}$

$=2\times 12 +2\times 7$

$=38\ \text{cm}$

$\text{Side length of square}$

$=\dfrac{38}{4}$

$=9.5\ \text{cm}$

Rectilinear Figures, SM-Bank 023 MC

A hexagon with equal sides and an equilateral triangle are drawn below.

3 identical hexagons and 8 identical equilateral triangles are connected as shown in the diagram below.

What is the perimeter of the larger shape?

$76.5\ \text{mm}$
$93.5\ \text{mm}$
$153\ \text{mm}$
$187\ \text{mm}$

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$D$

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$\text{Perimeter}$

$=\text{Number of sides}\times 8.5$

$=22\times 8.5$

$=187\ \text{mm}$

$\Rightarrow D$

Rectilinear Figures, SM-Bank 022

Joyce is walking her dog around a paddock in the shape of a parallelogram.

If she walks the dog around the paddock in the morning and the afternoon, how many kilometres do they walk each day? (2 marks)

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$14.8\ \text{km}$

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$\text{Perimeter of paddock}$

$=2\times 1.4+2\times 2.3$

$=7.4\ \text{km}$

$\text{Total distance walked each day}$

$=2\times 7.4$

$=14.8\ \text{km}$

Rectilinear Figures, SM-Bank 021 MC

The rhombus below has a side length $\large d$ .

Which expression cannot be used for the perimeter?

$2\times (d+d)$
$d\times 4$
$d\times d$
$d+d+2d$

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$C$

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$\text{Perimeter}=4\times d=4d$

$\text{Options A, B and D}=4d$

$\text{Option C}=d\times d=d^2\ne 4d$

$\Rightarrow C$

Rectilinear Figures, SM-Bank 020

Tatiana is cutting a piece of material in the shape of a parallelogram for a sewing project.

The longer sides are one and two-thirds times the length of the shorter sides.

What is the perimeter of the piece of material? (2 marks)

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$96\ \text{cm}$

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$\text{Longer side}$	$=\dfrac{5}{3}\times 18$
	$=30\ \text{cm}$

$\therefore\ \text{Perimeter}$	$=2\times 18 +2\times 30$
	$=96\ \text{cm}$

Rectilinear Figures, SM-Bank 019

Fumiko is laying pavers that are shaped like a parallelogram.

The longer sides are 3.5 times the length of the shorter sides.

What is the perimeter of one of the pavers? (2 marks)

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$72\ \text{cm}$

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$\text{Longer side}$	$=8\times 3.5$
	$=28\ \text{cm}$

$\therefore\ \text{Perimeter}$	$=2\times 8 +2\times 28$
	$=72\ \text{cm}$

Rectilinear Figures, SM-Bank 018

What is the perimeter of the shape below given each square has a side length of 2 cm? (2 marks)

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$40\ \text{cm}$

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$\text{Starting from bottom right moving clockwise.}$

$\text{Perimeter}$	$=12+2+2+2+2+2+6+4+2+6$
	$=40\ \text{cm}$

Rectilinear Figures, SM-Bank 017

A rectangular parking lot has a perimeter of 80 metres.

Each short side has a length of 10 metres.

What is the length of the long side? (2 marks)

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$30\ \text{m}$

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$\text{Let}\ \ d=\text{long side of parking lot}$

$2\times d + (2\times 10)$	$=80$
$2d$	$=80-20$
$2d$	$=60$
$\therefore\ d$	$=30\ \text{m}$

Rectilinear Figures, SM-Bank 016

A farmer uses an existing stone wall and fencing to create a large grazing paddock for his sheep, as shown in the diagram below.

The fencing has 3-strand wiring which is also shown below.

How many kilometres of wire will be required? (2 marks)

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$5.7\ \text{km}$

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$\text{Fencing required}$

$=3\times (450 + 200 + 150 + 500 + 600)$

$=3\times 1900$

$=5700\ \text{m}=5.7\ \text{km}$

Rectilinear Figures, SM-Bank 015

The length of this rectangle is one and a half times its height.

The perimeter of the rectangle is 40 centimetres.

What are the dimensions of the rectangle? (2 marks)

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$\text{Height}=8\ \text{cm}$

$\text{Length}=12\ \text{cm}$

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$\text{Let}\ \ \ x$	$=\text{height}$
$\dfrac{3}{2}x$	$=\text{length}$

$2\times \Big(x +\dfrac{3}{2}x\Big)$	$= 40$
$2\times \Big(\dfrac{5x}{2}\Big)$	$= 40$
$5x$	$= 40$
$x$	$= 8$

$\therefore\ \text{Height}$	$= 8\ \text{cm}$
$\therefore\ \text{Length}$	$=\dfrac{3}{2}\times 8$
	$=12\ \text{cm}$

Rectilinear Figures, SM-Bank 014

Ronald places 5 identical hexagonal tiles side-by-side to make the pattern pictured below.

Each tile has a perimeter of 24 cm and is in the shape of a regular hexagon.

What is the perimeter of the large shape, in centimetres? (2 marks)

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$64\ \text{cm}$

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$\text{Length of 1 side}$	$=\dfrac{24}{6}$
	$=4\ \text{cm}$

$\therefore\ \text{Perimeter}$	$=16\times 4$
	$=64\ \text{cm}$

Rectilinear Figures, SM-Bank 013

Aragorn is fencing a paddock on his property. The total length of fencing he requires is 8.2 kilometres.

The length of the paddock is 2.8 kilometres.

How wide is the paddock?

Write your answer, in kilometres to one decimal place? (2 marks)

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$1.3\ \text{km}$

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$\text{Express as a perimeter equation:}$

$2\times 2.8 + 2x$	$= 8.2$
$2x$	$= 8.2-5.6$
$2x$	$= 2.6$
$\therefore x$	$=1.3\ \text{km}$

$\therefore\ \text{Side length is }1.3\ \text{km}$

Rectilinear Figures, SM-Bank 012

Penelope made a shape using 6 identical squares.

What is the perimeter of the shape? (2 marks)

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$108\ \text{cm}$

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$\text{Length of 1 side}$	$=\dfrac{27}{3}$
	$=9\ \text{cm}$

$\therefore\ \text{Perimeter}$

$= (10\times 9) + (4\times 4.5)$

$= 90 + 18$

$=108\ \text{cm}$

Rectilinear Figures, SM-Bank 011

This shape is made from eight equilateral triangles and one large parallelogram.

Each side of all the small triangles is 4 cm long.

What is the perimeter of the shape? (2 marks)

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$48\ \text{cm}$

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$\text{Perimeter from the top left corner (clockwise)}$

$=12+4+4+4+4+8+4+8$

$=48\ \text{cm}$

Rectilinear Figures, SM-Bank 010

A rectangle has a length of 25 cm and a width of 20 cm.

A square has the same perimeter as this rectangle.

What is the side length of this square in centimetres? (2 marks)

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$22.5\ \text{cm}$

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$\text{Perimeter of rectangle}$	$= (2\times 25) + (2\times 20)$
	$=90\ \text{cm}$

$\therefore\ \text{Side length of square}$	$=\dfrac{90}{4}$
	$=22.5\ \text{cm}$

Rectilinear Figures, SM-Bank 009 MC

A regular hexagon is drawn below.

5 identical hexagons are connected as shown in the diagram below.

What is the perimeter of the larger shape?

$110\ \text{cm}$
$121\ \text{cm}$
$132\ \text{cm}$
$165\ \text{cm}$

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$B$

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$\text{Perimeter}$	$=\text{Number of sides}\times 5.5$
	$=22\times 5.5$
	$=121\ \text{cm}$

$\Rightarrow B$

Rectilinear Figures, SM-Bank 008 MC

What is the perimeter of this shape?

$44\ \text{cm}$
$47\ \text{cm}$
$60\ \text{cm}$
$146\ \text{cm}$

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$C$

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$\text{Perimeter (clockwise from top left corner)}$

$= 8 + 8 + 6 + 5 + 10 + 3 + 4 + 16$

$= 60\ \text{cm}$

$\Rightarrow C$

Rectilinear Figures, SM-Bank 007 MC

A shape, pictured below, is made with 5 rhombuses.

What is the perimeter of the shape?

$10\ \text{cm}$
$14\ \text{cm}$
$12\ \text{cm}$
$20\ \text{cm}$

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$C$

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$\text{All sides of a rhombus are equal}$

$\text{Perimeter}$	$=12\times 1$
	$=12\ \text{cm}$

$\Rightarrow C$

Rectilinear Figures, SM-Bank 006

A rectangular car park is shown below with a perimeter of 70 m.

What is the length of the short side $\large x$? (2 marks)

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$10\ \text{m}$

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$\text{Perimeter}$	$=25 + 25 + x +x$
$70$	$=50 + 2x$
$2x$	$=70-50=20$
$\therefore x$	$=10\ \text{m}$

Rectilinear Figures, SM-Bank 005 MC

Andrew drew a shape as pictured below.

What is the perimeter of this shape in centimetres?

$101$
$127$
$148$
$154$

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$D$

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$\text{Starting at the bottom left corner and}$

$\text{moving clockwise:}$

$\text{Perimeter}$	$= 26 + 30 + 26 + 8 + 21 + 16 + 21 + 6$
	$= 154\ \text{cm}$

$\Rightarrow D$

Rectilinear Figures, SM-Bank 004

Justin connects three of his restaurant tables together to make one long table.

The view from above the tables is shown below.

Each table is 70 cm long and 50 cm wide.

What is the perimeter of the long table? (2 marks)

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$520\ \text{cm}$

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$\text{Perimeter}$	$= 2\times (210 + 50)$
	$= 2\times 260$
	$= 520\ \text{cm}$

Rectilinear Figures, SM-Bank 003 MC

The table shows the dimensions of four different rectangles in centimetres.

Rectangle	Length (cm)	Width (cm)
1	9	5
2	10	8
3	14	2
4	18	10

Which rectangle has a perimeter of 28 centimetres?

Rectangle 1
Rectangle 2
Rectangle 3
Rectangle 4

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$A$

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$\text{Consider rectangle 1}$

$\text{Perimeter}$	$= 2\times \text{length} + 2\times \text{width}$
	$= (2\times 9) + (2\times 5)$
	$=28\ \text{cm}$

$\therefore\ \text{Rectangle 1 has a perimeter of 28 cm.}$

$\Rightarrow A$

Rectilinear Figures, SM-Bank 002 MC

Which one of these shapes has the largest perimeter?

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$B$

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$\text{Consider Option B:}$

$\text{Perimeter}$	$=3\times 4+3\times 2+2\times 1$
	$=20\ \text{units}$

$\Rightarrow B$

Rectilinear Figures, SM-Bank 001 MC

What is the perimeter of the shape below given each square has a side length of 1 cm?

$8\ \text{cm}$
$18\ \text{cm}$
$20\ \text{cm}$
$36\ \text{cm}$

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$C$

Show Worked Solution

$\text{Starting at the bottom right corner and}$

$\text{moving clockwise:}$

$\text{Perimeter}$	$=5+3+1+2+1+2+1+2+2+1$
	$=20\ \text{cm}$

$\Rightarrow C$

\(\text{Then,}\ \ 2\times x+4\)	\(=20\)
\(2x\)	\(=20-4\)
\(2x\)	\(=16\)
\(x\)	\(=8\)

\(2\times d + (2\times 10)\)	\(=80\)
\(2d\)	\(=80-20\)
\(2d\)	\(=60\)
\(\therefore\ d\)	\(=30\ \text{m}\)

\(\text{Let}\ \ \ x\)	\(=\text{height}\)
\(\dfrac{3}{2}x\)	\(=\text{length}\)

\(2\times \Big(x +\dfrac{3}{2}x\Big)\)	\(= 40\)
\(2\times \Big(\dfrac{5x}{2}\Big)\)	\(= 40\)
\(5x\)	\(= 40\)
\(x\)	\(= 8\)

\(\therefore\ \text{Height}\)	\(= 8\ \text{cm}\)
\(\therefore\ \text{Length}\)	\(=\dfrac{3}{2}\times 8\)
	\(=12\ \text{cm}\)

\(\text{Longer side}\)	\(=\dfrac{5}{3}\times 18\)
	\(=30\ \text{cm}\)

\(\therefore\ \text{Perimeter}\)	\(=2\times 18 +2\times 30\)
	\(=96\ \text{cm}\)

\(\text{Longer side}\)	\(=8\times 3.5\)
	\(=28\ \text{cm}\)

\(\therefore\ \text{Perimeter}\)	\(=2\times 8 +2\times 28\)
	\(=72\ \text{cm}\)