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Area, SM-Bank 080

Bobby used 3 litres of varnish to paint the loungeroom floor.

The floor was a square with sides 6 metres long.

How many litres of varnish would he need to paint a rectangular floor which is 6 metres long and 10 metres wide?  (2 marks)

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\(5\ \text{litres}\)

Show Worked Solution

\(\text{Area of square floor}\)

\(=6^2\)

\(=36\ \text{m}^2\)

\(\text{Area of rectangular floor}\)

\(=6\times 10\)

\(=60\ \text{m}^2\)

\(\text{Paint needed for rectangular wall}\)

\(=\dfrac{60}{36}\times 3\)

\(=5\ \text{litres}\)

Area, SM-Bank 079

Shinji used 8 litres of paint to paint a wall.

The wall was a square with sides 4 metres long.

How many litres of paint would he need to paint a rectangular wall which is 3 metres high and 10 metres wide?  (2 marks)

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\(15\ \text{litres}\)

Show Worked Solution

\(\text{Area of square wall}\)

\(=4^2\)

\(=16\ \text{m}^2\)

\(\text{Area of rectangular wall}\)

\(=3\times 10\)

\(=30\ \text{m}^2\)

\(\text{Paint needed for rectangular wall}\)

\(=\dfrac{30}{16}\times 8\)

\(=15\ \text{litres}\)

Area, SM-Bank 078

Shinji used 8 litres of paint to paint a wall.

The wall was a square with sides 4 metres long.

How many litres of paint would he need to paint a rectangular wall which is 3 metres high and 10 metres wide?  (2 marks)

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\(15\ \text{litres}\)

Show Worked Solution

\(\text{Area of square wall}\)

\(=4^2\)

\(=16\ \text{m}^2\)

\(\text{Area of rectangular wall}\)

\(=3\times 10\)

\(=30\ \text{m}^2\)

\(\text{Paint needed for rectangular wall}\)

\(=\dfrac{30}{16}\times 8\)

\(=15\ \text{litres}\)

Area, SM-Bank 056

A sporting field in the shape of a square has a side length of 110 metres.

  1. Calculate the area of the sporting field in square metres.  (2 marks)

  2. During the off-season, the sporting field is to be covered in fertiliser. If fertiliser costs $6.50 per 100 square metres, calculate the cost of fertilising the field.  (2 marks)

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a.    \(12\ 100\ \text{m}^2\)

b.    \($786.50\)

Show Worked Solution
a.    \(\text{Area}\) \(=s^2\)
    \(=110^2\)
    \(=12\ 100\ \text{m}^2\)

 

b.    \(\text{Cost}\) \(=\dfrac{12\ 100}{100}\times 6.50\)
    \(=121\times 6.50\)
    \(=$786.50\)

Area, SM-Bank 055

The square below has a diagonal of 12 metres.

  1. Use Pythagoras' Theorem to calculate the side length of the square. Give your answer in exact surd form.  (2 marks)


  2. Calculate the are of the square correct to one decimal place.  (2 marks)

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a.    \(\sqrt{72}\ \text{m}\)

b.    \(72\ \text{m}^2\)

Show Worked Solution

a.    \(\text{Using Pythagoras to find the side length of the square:}\)

\(a^2+b^2\) \(=c^2\)
\(a^2+a^2\) \(=12^2\)
 \(2a^2\) \(=144\)
\(a^2\) \(=\dfrac{144}{2}=72\)
 \(a\) \(=\sqrt{72}\ \text{m}\)

b.   

\(\text{Area}\) \(=s^2\)
  \(=(\sqrt{72})^2\)
  \(=72\ \text{m}^2\)

Area, SM-Bank 054

Calculate the area of a square with a perimeter of 192 centimetres.  (2 marks)

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\(2304\ \text{cm}^2\)

Show Worked Solution
\(\text{Perimeter}\) \(=192\ \text{cm}\)
\(\therefore\ \text{Side}\) \(=\dfrac{192}{4}\)
  \(=48\ \text{cm}\)

 

\(\text{Area}\) \(=s^2\)
  \(=48^2\)
  \(=2304\ \text{cm}^2\)

Area, SM-Bank 053

The following shape has a perimeter of 12.4 centimetres. Calculate its' area.  (2 marks)

 

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\(9.61\ \text{cm}^2\)

Show Worked Solution
\(\text{Perimeter}\) \(=12.4\ \text{cm}\)
\(\therefore\ \text{Side}\) \(=\dfrac{12.4}{4}\)
  \(=3.1\ \text{cm}\)

 

\(\text{Area}\) \(=s^2\)
  \(=3.1^2\)
  \(=9.61\ \text{cm}^2\)

Area, SM-Bank 052

The following shape has a perimeter of 36 metres. Calculate its' area.  (2 marks)

 

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\(81\ \text{m}^2\)

Show Worked Solution
\(\text{Perimeter}\) \(=36\ \text{m}\)
\(\therefore\ \text{Side}\) \(=\dfrac{36}{4}\)
  \(=9\ \text{m}\)

 

\(\text{Area}\) \(=s^2\)
  \(=9^2\)
  \(=81\ \text{m}^2\)

Area, SM-Bank 051

Calculate the area of the following squares.

  1.  
      (2 marks)

  2.  
      (2 marks)

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a.    \(151.29\ \text{cm}^2\)

b.    \(3.24\ \text{m}^2\)

Show Worked Solution
a.    \(\text{Area}\) \(=s^2\)
    \(=12.3^2\)
    \(=151.29\ \text{cm}^2\)

 

b.    \(\text{Area}\) \(=s^2\)
    \(=1.8^2\)
    \(=3.24\ \text{m}^2\)

Area, SM-Bank 050

Calculate the area of the following squares.

  1.  
        (2 marks)

     
  2.  
       (2 marks)

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a.    \(64\ \text{cm}^2\)

b.    \(20\ 164\ \text{mm}^2\)

Show Worked Solution
a.    \(\text{Area}\) \(=s^2\)
    \(=8^2\)
    \(=64\ \text{cm}^2\)

 

b.    \(\text{Area}\) \(=s^2\)
    \(=142^2\)
    \(=20\ 164\ \text{mm}^2\)

Area SM-Bank 049

A rectangle has an area of 24 square centimetres.

  1. One possible pair of integer dimensions for this rectangle is \(2\ \text{cm}\times 12\ \text{cm}\).
    Write down all possible pairs of integer dimensions for a rectangle with an area of 24 square centimetres.  (2 marks)

  2. Using the given dimensions and your answers from (a), calculate the largest possible perimeter for a rectangle with an area of 24 square centimetres.  (2 marks)


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a.    \(1\ \text{cm}\times 24\ \text{cm}, 2\ \text{cm}\times 12\ \text{cm}, 3\ \text{cm}\times 8\ \text{cm}, 4\ \text{cm}\times 6\ \text{cm}\)

b.    \(50\ \text{cm}\)

Show Worked Solution

a.    \(\text{All possible integer dimensions:}\)

\(1\ \text{cm}\times 24\ \text{cm},\ \ 2\ \text{cm}\times 12\ \text{cm},\ \ 3\ \text{cm}\times 8\ \text{cm},\ \ 4\ \text{cm}\times 6\ \text{cm}\)

b.    \(\text{Perimeters}\)

\(\text{P}_{1}=2\times 1+2\times 24=50\ \text{cm}\)

\(\text{P}_{2}=2\times 2+2\times 12=28\ \text{cm}\)

\(\text{P}_{3}=2\times 3+2\times 8=22\ \text{cm}\)

\(\text{P}_{4}=2\times 4+2\times 6=20\ \text{cm}\)

\(\therefore\ \text{Largest possible perimeter}= 50\ \text{cm}\)

Area, SM-Bank 048

Jocasta is sewing a quilt in the shape of a rectangle, as shown below. She knows the length of one side, and the length of diagonal of the quilt.

  1. Calculate the length of the other side of the quilt, giving your answer in exact surd form.  (2 marks)

  2. Using your answer from (a) calculate the area of the quilt in square metres, correct to 1 decimal place?  (2 marks)


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a.    \(\sqrt{2.05}\ \text{m}\)

b.    \(2.6\ \text{m}^2\ (1\ \text{d.p.})\)

Show Worked Solution

a.    \(\text{Using Pythagoras to find the shorter side:}\)

\(a^2+b^2\) \(=c^2\)
\(a^2+1.8^2\) \(=2.3^2\)
 \(a^2\) \(=2.3^2-1.8^2\)
\(a^2\) \(=2.05\)
 \(a\) \(=\sqrt{2.05}\ \text{m}\)

 

b.    \(\text{Area}\) \(=l\times b\)
    \(=1.8\times \sqrt{2.05}\)
    \(=2.577\dots\)
    \(=2.6\ \text{m}^2\ (1\ \text{d.p.})\)

Area, SM-Bank 047

Jordy is tiling the rectangular living area pictured below.

  1. Calculate the area of the living area in square metres.  (2 marks)

  2. What is the cost of tiling the living area if tiles cost $45 per square metre?  (2 marks)

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a.    \(25.84\ \text{m}^2\)

b.    \($1162.80\)

Show Worked Solution
a.    \(\text{Area}\) \(=l\times b\)
    \(=7.6\times 3.2\)
    \(=25.84\ \text{m}^2\)

 

b.    \(\text{Cost}\) \(=\text{price per square metre}\times \text{number of square metres}\)
    \(=$45\times 25.84\)
    \(=$1162.80\)

Area, SM-Bank 046

A rectangular paddock has dimensions 1.2 kilometres by 1.4 kilometres. Calculate the area of the paddock in square kilometres.  (2 marks)

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\(1.68\ \text{km}^2\)

Show Worked Solution
\(\text{Area}\) \(=l\times b\)
  \(=1.2\times 1.4\)
  \(=1.68\ \text{km}^2\)

Area, SM-Bank 045

Calculate the area of the following rectangles, correct to 1 decimal place.

  1.  
        (2 marks)

  2.  
       (2 marks)

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a.    \(82.1\ \text{m}^2\ (1\ \text{d.p.})\)

b.    \(1023.8\ \text{mm}^2\ (1\ \text{d.p.})\)

Show Worked Solution
a.    \(\text{Area}\) \(=l\times b\)
    \(=7.2\times 11.4\)
    \(=82.08\)
    \(=82.1\ \text{m}^2\ (1\ \text{d.p.})\)

 

b.    \(\text{Area}\) \(=l\times b\)
    \(=67.8\times 15.1\)
    \(=1023.78\)
    \(=1023.8\ \text{mm}^2\ (1\ \text{d.p.})\)

Area, SM-Bank 044

Calculate the area of the following shapes in square centimetres.

  1.   
       (2 marks)

  2.   
       (2 marks)

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a.    \(78\ \text{cm}^2\)

b.    \(274\ \text{cm}^2\)

Show Worked Solution
a.    \(\text{Area}\) \(=l\times b\)
    \(=13\times 6\)
    \(=78\ \text{cm}^2\)

 

b.    \(\text{Area}\) \(=l\times b\)
    \(=10\times 27.4\)
    \(=274\ \text{cm}^2\)

Area, SM-Bank 043

Calculate the area of the following shapes in square units.

  1.  
              (1 mark)

     

  2.       
            (1 mark)

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a.    \(12\ \text{square units}\)

b.    \(10\ \text{square units}\)

Show Worked Solution

a.    \(\text{Area}=4\times 3=12\ \text{square units}\)

b.    \(\text{Area}\) \(=\text{Triangle }1+\text{Triangle }2\)
    \(=\dfrac{1}{2}\times 15+\dfrac{1}{2}\times 5\)
    \(=10\ \text{square units}\)

 

Area, SM-Bank 026 MC

David's backyard is in shape of a rectangle and has an area of \(50\ \text{m}^2\).

Tim's backyard is also rectangular but with side lengths that are double those of David's backyard.

What is the area of Tim's backyard.

  1. \(25\ \text{m}^2\)
  2. \(100\ \text{m}^2\)
  3. \(200\ \text{m}^2\)
  4. \(300\ \text{m}^2\)
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\(C\)

Show Worked Solution

\(\text{Let the dimensions of David’s yard be:}\ \ x, y\)

\(\text{Area} =x\times y\)

  
\(\Longrightarrow\ \text{Tim’s yard’s dimensions are:}\ \ 2x, 2y\)

\(\text{Area}\) \(=2x\times 2y\)
  \(=4\times xy\)
  \(= 4\times 50\)
  \(= 200\ \text{m}^2\)

 
\(\Rightarrow C\)

Area, SM-Bank 025 MC

Mark decides to make the paddock on his farm bigger.

The paddock is in the shape of a rectangle.

Mark makes both the length and the width of the paddock 3 times longer.

How many times bigger is the area of the new paddock than the original paddock?

  1. \(3\)
  2. \(4\)
  3. \(6\)
  4. \(9\)
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\(D\)

Show Worked Solution

\(\text{Area of original paddock}=l\times b\)

\(\text{Area of new paddock}\) \(=3l\times 3b\)
  \(=9\times (l\times b)\)
  \(=9\times \text{Area of original paddock}\)

\(\Rightarrow D\)

Area, SM-Bank 024

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 area of this square in square centimetres?  (2 marks)

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\(506.25\ \text{cm}^2\)

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

 

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

 

\(\therefore\ \text{Area of square}\) \(=\text{(side)}^2\)
  \(=22.5^2\)
  \(=506.25\ \text{cm}^2\)

Area, SM-Bank 021

A square has an area of \(81\ \text{cm}^2\).

A rectangle has the same perimeter as the square and has a width of \(15\ \text{cm}\).

What is the length of the rectangle in centimetres?  (2 marks)

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\(3\ \text{cm}\)

Show Worked Solution

\(\text{Area of square} = 81\ \text{cm}^2\)

\(\therefore\ \text{Side length of square}=\sqrt{81}=9\ \text{cm}\)

\(\therefore\ \text{Perimeter of square}=4\times 9=36\ \text{cm}\)

\(\therefore\ \text{Length of rectangle}\) \(=\dfrac{36-(2\times 15)}{2}\)
  \(=\dfrac{6}{2}\)
  \(=3\ \text{cm}\)

Area, SM-Bank 020

Dave has a backyard in the shape of a rectangle.
 

   
 

The longer side is  \(1\dfrac{1}{3}\)  times longer than the shorter side.

What is the area of Dave’s backyard?  (2 marks)

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\(588\ \text{m}^2\)

Show Worked Solution
\(\text{Longer side}\) \(=21\times \dfrac{4}{3}\)
  \(=28\ \text{m}\)

 

\(\therefore\ \text{Area}\) \(=21\times 28\)
  \(=588\ \text{m}^2\)

Area, SM-Bank 019 MC

Brock decided to cut out a small rectangle from a piece of patterned rectangular paper.

The rectangle cut out has a length of 60 mm and a height of 40 mm.

Which of the following expressions gives the area of patterned paper that was left after cutting out the smaller rectangle?
 

  1. \((120\times 200)-(60\times 160)\)
  2. \((60\times 160)\)
  3. \((120\times 200)-(40\times 160)\)
  4. \((120\times 200)-(60\times 40)\)

Show Answers Only

\(D\)

Show Worked Solution
\(\text{Area}\) \(=\text{Area of large rectangle}-\text{Area of small rectangle}\)
  \(=(120\times 200)-(60\times 40)\)

 
\(\Rightarrow D\)

Area, SM-Bank 018

Airships are a form of aircraft.

An airship has a cabin in which the pilots and passengers travel, and cargo is carried. This is shown in the simplified diagram below.
 

The floor of the cabin is a rectangle, with a length of 9 m and a width of 2.5 m.

The cockpit occupies an area 1.5 m by 2.5 m at the front of the cabin. This is shown shaded in the diagram below.

The remainder of the floor space is available for passengers and cargo.
 

Calculate the area available for passengers and cargo, in square metres.  (2 marks)

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\(18.75\ \text{m}^2\)

Show Worked Solution
\(\text{Area}\) \(=9\times 2.5-1.5\times 2.5\)
  \(=22.5-3.75\)
  \(=18.75\ \text{m}^2\)

Area, SM-Bank 010

A square has an area of 169 square centimetres.

What is the perimeter?  (2 marks)

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\(52\ \text{cm}\)

Show Worked Solution

\(\text{Let}\ \ s=\text{side length of the square}\)

\(\text{Area:}\rightarrow\ \ s^2\) \(=169\)
\(s\) \(=\sqrt{169}\)
  \(=13\ \text{cm}\)

 

\(\therefore\ \text{Perimeter}\) \(=4\times 13\)
  \(=52\ \text{cm}\)

Area, SM-Bank 008

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

 
The perimeter of the rectangle is 50 centimetres.

What is the area of the rectangle?  (2 marks)

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\(150\ \text{cm}^2\)

Show Worked Solution

\(\text{Let}\ x=\text{width, then}\ \ 1.5x=\text{length}\)

\(\text{Perimeter:}\ \rightarrow\ \) \(\ \ 2\times x+2\times 1.5 x\) \(=50\)
  \(5x\) \(=50\)
  \(x\) \(=10\)

\(\therefore\ \text{width}=10\ \text{cm,  length}=15\ \text{cm}\)

\(\therefore\ \text{Area}\) \(=10\times 15\)
  \(=150\ \text{cm}^2\)

Area, SM-Bank 005

The area of the shaded rectangle below is \(84\ \text{cm}^2\).
 

 
What is the length of the shaded rectangle?  (2 marks)

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\(14\ \text{cm}\)

Show Worked Solution

\(\text{Let}\ \ l =\text{length of rectangle}\)

\(l\times 6\) \(=84\)
\(\therefore\ l\) \(=\dfrac{84}{6}\)
  \(=14\ \text{cm}\)

Area, SM-Bank 004 MC

A neighbourhood soccer oval is marked out with the dimensions shown below.
 

 
What is the area of the field?

  1. \(298\ \text{m}^2\)
  2. \(2842.75\ \text{m}^2\)
  3. \(5261.25\ \text{m}^2\)
  4. \(8123.25\ \text{m}^2\)
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Area of the soccer field}\)

\(=57.5\times 91.5\)

\(= 5261.25\ \text{m}^2\)

\(\Rightarrow C\)

Area, SM-Bank 003 MC

A resort has 4 pools.

Which pool has the largest surface area?
 

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\(D\)

Show Worked Solution

\(\text{Consider the surface area of each pool:}\)

\(\text{Pool A}=6\times 19=114\ \text{m}^2\)

\(\text{Pool B}=7\times 18=126\ \text{m}^2\)

\(\text{Pool C}=10\times 15=150\ \text{m}^2\)

\(\text{Pool D}=12.5\times 12.5=156.25\ \text{m}^2\)

 
\(\therefore\ \text{Pool D,}\ 12.5\times 12.5,\text{ has the largest}\)

\(\text{surface area.}\)

\(\Rightarrow D\)

Area, SM-Bank 002 MC

Bob had a mini tennis court in his backyard, as shown in the diagram below.
 

What is the area of the mini tennis court?

  1. \(6\ \text{m}^2\)
  2. \(12\ \text{m}^2\)
  3. \(24\ \text{m}^2\)
  4. \(48\ \text{m}^2\)
Show Answers Only

\(C\)

Show Worked Solution

\(\text{The mini tennis court has dimensions}\ \ 6\times 4\)

\(\therefore\ \text{Area}\) \(=6\times 4\)
  \(=24\ \text{m}^2\)

 
\(\Rightarrow C\)