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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 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?

  1. \(76.5\ \text{mm}\)
  2. \(93.5\ \text{mm}\)
  3. \(153\ \text{mm}\)
  4. \(187\ \text{mm}\)
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\(D\)

Show Worked Solution

\(\text{Perimeter}\)

\(=\text{Number of sides}\times 8.5\)

\(=22\times 8.5\)

\(=187\ \text{mm}\)

\(\Rightarrow D\)

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 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 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 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?

  1. \(110\ \text{cm}\)
  2. \(121\ \text{cm}\)
  3. \(132\ \text{cm}\)
  4. \(165\ \text{cm}\)
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\(B\)

Show Worked Solution
\(\text{Perimeter}\) \(=\text{Number of sides}\times 5.5\)
  \(=22\times 5.5\)
  \(=121\ \text{cm}\)

\(\Rightarrow B\)

Rectilinear Figures, SM-Bank 001 MC

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

  1. \(8\ \text{cm}\)
  2. \(18\ \text{cm}\)
  3. \(20\ \text{cm}\)
  4. \(36\ \text{cm}\)
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\(C\)

Show Worked Solution

\(\text{Starting at the bottom right corner and}\)

\(\text{moving clockwise:}\)

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

\(\Rightarrow C\)