Jason draws an irregular shape as shown below.
What is the perimeter of this shape in metres?

113 m 

131 m 

134 m 

136m 

143 m 
Aussie Maths Teachers: Save your time with SmarterMaths
Jason draws an irregular shape as shown below.
What is the perimeter of this shape in metres?

113 m 

131 m 

134 m 

136m 

143 m 
`134\ text{m}`
`text{Perimeter}`  `= 8+10+3+18+19+12+24+40 ` 
`= 134 \ text{metres}` 
Trisha cuts out a triangular shape from a rectangular piece of cardboard.
The triangle has a height of 2 cm and base of 8 cm.
Which of the following expression gives the area of Trisha’s cardboard after cutting out the triangle?

`(32 xx 60)  (8 xx 2)` 

`(52 xx 30)` 

`(32 xx 60)  (1/2 xx 8 xx 2)` 

`(60 xx 32)  (1/2 + 8 + 2)` 
`(32 xx 60)  (1/2 xx 8 xx 2)`
`text(Area)`  `= text(Area of rectangle)  text(Area of triangle)` 
`= (32 xx 60)  (1/2 xx 8 xx 2)` 
The picture below is a shape made with 7 equilateral triangles.
What is its perimeter?

16 cm 

18 cm 

19 cm 

20 cm 
`text{18 cm}`
`text(Equilateral triangle → all sides are equal.)`
`text{Perimeter}`  `= text{Number of sides} xx 2 \ text{cm}` 
`= 9 xx 2`  
`= 18 \ text{cm}` 
Leo painted the patterns shown below.
All the triangles that make up the shape have the same area.
Which of the following has the largest area painted grey?







`text(Largest area painted → most triangles painted grey.)`
`text(Checking each option:)`
`text(Option 1  12 triangles painted)`
`text(Option 2  10 triangles painted)`
`text(Option 3  12 triangles painted)`
`text{Option 4  14 triangles painted (largest area)}`
What shape has an area greater than 11 square units?

A 

B 

C 

D 
`A`
`text{Area of triangle} = frac{1}{2} xx text{b} xx text{h}`
`text{Check each option:}`
`text{A.} \ frac{1}{2} xx 6 xx 4 = 12 \ text{(Correct)}`
`text{B.} \ frac{1}{2} xx 3 xx 3 = 4.5`
`text{C} \ frac{1}{2} xx 6 xx 3 = 9`
`text{D} \ frac{1}{2} xx 4 xx 4 = 8`
`therefore \ text{triangle A has an area greater than 11 square units.}`
In a suburb, four families measured the dimensions of their rectangular backyards.
Which backyard has the largest area?







`text(Checking each option:)`
`text(Option 1:)\ 11 xx 18 = 198 text(m)^2`
`text(Option 2:)\ 16 xx 6 = 96 text(m)^2`
`text(Option 3:)\ 15 xx 10 = 150 text(m)^2`
`text(Option 4:)\ 14 xx 12 = 168 text(m)^2`
`:. text(The backyard with the largest area is the)\ 11\ text(m) xx 18\ text(m)`
`text(with a total area of 198 square metres.)`
A shape, pictured below, is made up of 6 equilateral triangles.
What is the perimeter of the shape?
12 cm  20 cm  24 cm  36 cm 




`24\ text(cm)`
`text(S)text(ince all sides of an equilateral triangle are equal,)`
`text(Perimeter)\ = 6 xx 4 = 24\ text(cm)`
A shape, pictured below, is made with 5 rhombuses.
What is the perimeter of the shape?
10 cm  12 cm  20 cm  24 cm 




`24\ text(cm)`
`text(S)text(ince all sides of a rhombus are equal,)`
`text(Perimeter)\ = 12 xx 2 = 24\ text(cm)`
Jenna is designing a stage in the shape of a rectangle.
She wants the stage to be at least 18 square metres.
She has made two sides of the stage each 6.5 metres in length.
What is the smallest possible length of each of the other two sides, rounded to one decimal place?
2.6 metres  2.8 metres  3 metres  3.2 metres 




`text(2.8 metres)`
`text(Let)\ \ d =\ text(length of other side)`
`6.5 xx d`  `>= 18` 
`d`  `>= 18/6.5` 
`d`  `>= 2.76…\ text(m)` 
`:.\ text{Smallest length is 2.8 m (to 1 d.p.)}`
Martin is designing a rectangular pool.
He wants the pool surface to be at least 48 square metres.
He has dug out two sides each 8.3 metres in length.
What is the smallest possible length of each of the other two sides, rounded to one decimal place?
6 metres  5.8 metres  5.5 metres  5 metres 




`text(5.8 metres)`
`text(Let)\ \ d =\ text(length of other side)`
`8.3 xx d`  `>= 48` 
`d`  `>= 48/8.3` 
`d`  `>= 5.78…\ text(m)` 
`:.\ text{Smallest length is 5.8 m (to 1 d.p.)}`
A square has a perimeter of 84 cm.
A rectangle has the same perimeter as the square and has a width of 15cm.
What is the length of the rectangle in centimetres?
`10`  `20`  `27`  `42` 




`27\ text(cm)`
`text(Perimeter of square) = 84\ text(cm)`
`:.\ text(Length of rectangle)`  `= (84  (2 xx 15))/2` 
`= 54/2`  
`=27\ text(cm)` 
A rectangle has width of 12 cm and a length of 26 cm
A square has the same perimeter as the rectangle
What is the length of each side of the square in centimetres?
`14`  `19`  `20`  `28` 




`19\ text(cm)`
`text(Perimeter of rectangle)`  `= (2 xx 12) + (2 xx 26)` 
`=76\ text(cm)` 
`:.\ text(Side length of square)`  `=76/4` 
`=19\ text(cm)` 
There are 4 pools pictured below.
Which pool, including the tiled edge, has the largest surface area?




`C`
`text{Surface area of each picture frame:}`
`text{1st pool: } 20 \times 6 = 108`
`text{2nd pool: } 12\times 18 = 216`
`text{3rd pool: } 16 \times 16 = 256`
`text{4th pool: } 20 \times 12 = 240`
`\therefore \ \ text{picture of 3rd pool has the largest surface area.} `
There are 4 picture frames shown below.
Which frame has the largest area?




`text{Surface area of each picture frame:}`
`text{1st frame: } 20 \times 15 = 300`
`text{2nd frame: }10 \times 25 = 250`
`text{3rd frame: }15 \times 15 = 225`
`text{4th frame: }24 \times 8 = 192`
`\therefore \ \ text{picture of 1st frame has the largest surface area.} `
A cube has a surface area of 384 square centimetres.
What is the volume of the cube?
cubic centimetres 
`512\ text(cm³)`
`text(Cube has 6 faces.)`
`text(Area of 1 face)`  `= 384 : 6` 
`= 64\ text(cm²)`  
`text(Side length)`  `= sqrt 464` 
`= 8\ text(cm)` 
`:.\ text(Volume)`  `=8^3` 
`= 512\ text(cm³)` 
Luke designs a table that is in the shape of a trapezium.
The dimensions of the top of the table in the picture below.
What is the area of Luke's table top?
cm² 
`880\ text(cm²)`
`text(Area)`  `=\ text(Area of rectangle + 2 × Area of triangle)` 
`= (38 xx 20) + 2 xx (1/2 xx 6 xx 20)`  
`= 760 + 120`  
`= 880\ text(cm²)` 
The beaker pictured below can hold up to 100 millilitres of hydrochloric acid.
How much hydrochloric acid is in the beaker?

70 mL 

75 mL 

80 mL 

85 mL 
`85 \ text{mL}`
`text{Beaker is fully filled to the 70 mL mark}`
`text{Beaker is half filled between 70 – 100 mL}`
`therefore \ text{Volume}`  `= 70 + frac{1}{2} xx 30` 
`= 70 + 15`  
`= 85 \ text{mL}` 
Ken made these solid prisms out of identical cubes.
Which prism has the largest volume?




`text{Volume of each prism:}`
`text(Option 1: 5 × 2 × 3 = 30 cubes)`
`text(Option 2: 3 × 3 × 3 = 27 cubes)`
`text(Option 3: 7 × 2 × 2 = 28 cubes)`
`text(Option 4: 4 × 4 × 2 = 32 cubes)`
`:.\ text(The prism with the largest volume is)`
The length of this rectangle is one and a half times its height.
The perimeter of the rectangle is 50 centimetres.
What is the area of the rectangle?
square centimetres 
`150\ text(cm²)`
`text(Let)\ x`  `=\ text(height)` 
`3/2 x`  `=\ text(length)` 
`2 xx (x + 3/2 x)`  `= 50` 
`5x`  `= 50` 
`x`  `= 10` 
`:.\ text(Area)`  `= 10 xx 15` 
`= 150\ text(cm²)` 
Crystal drew a shape as pictured below.
What is the perimeter of this shape in centimetres?
`73`  `90`  `108`  `112`  `122` 





`112\ text(cm)`
`text(Starting at the bottom left corner and)`
`text(moving clockwise:)`
`text(Perimeter)`  `= 18 + 24 + 18 + 7 + 14 + 12 + 14 + 5` 
`= 112\ text(cm)` 
Squares with sides 5 cm are cut out from the corners of a rectangular piece of cardboard.
The sides are then folded to make a rectangular box with no lid.
What is the volume of the box?
`text(12 cm³)`  `text(60 cm³)`  `text(72 cm³)`  `text(96 cm³)`  `text(120 cm³)` 





`60\ text(cm³)`
`text(Volume)`  `=\ text(base area × height)` 
`= (6 xx 2) xx 5`  
`= 60\ text(cm³)` 
Which of these could be used to calculate the area of the shape in square centimetres?
`(7 xx 2) + (10 xx 9)`  `(10 xx 7) + (10 xx 2)` 


`(10 xx 7) + (7 xx 3)`  `(10 xx 9)  (3 xx 2)` 


`(10 xx 9)  (3 xx 2)`
`text(Area)`  `=\ text(Area of large rectangle – Area of cutout rectangle)` 
`=(10 xx 9)  (3 xx 2)` 
Michael designs an outdoor table that is in the shape of a trapezium.
The dimensions of the table top are shown in the picture below.
What is the area of Michael's table top?
cm² 
`3600\ text(cm²)`
`text(Area)`  `=\ text(Area of rectangle + 2 × Area of triangle)` 
`= (45 xx 65) + 2 xx (1/2 xx 15 xx 45)`  
`=2925 + 675`  
`= 3600\ text(cm²)` 
Two identical solid cubes are placed at the bottom of a fish tank.
The fish tank is then completely filled, as shown below.
What is the volume of the water that surrounds the cubes?
Give your answer in cubic centimetres.
cm^{3} 
`220\ 544\ text(cm)^3`
`text(Volume of tank)`  `= 70 xx 40 xx 80` 
`= 224\ 000\ text(cm)^3` 
`text(Volume of cubes)`  `= 2 xx 12 xx 12 xx 12` 
`= 3456\ text(cm)^3` 
`:.\ text(Volume of water)`  `= 224\ 000  3456` 
`= 220\ 544\ text(cm)^3` 
A block is in the shape of a prism.
Its surface is covered in triangles.
How many triangles cover the entire surface of the block?
triangles 
`48`
`text(Triangles on 1 end = 6)`
`text(Triangles on 1 side = 6)`
`text(Total triangles)`  `= (6 xx 2) + (6 xx 6)` 
`= 12 + 36`  
`= 48` 
A cube has a total surface area of 294 square centimetres.
What is the volume of the cube?
cubic centimetres 
`343\ text(cm³)`
`text(Cube has 6 faces.)`
`text(Area of 1 face)`  `= 294:6` 
`= 49\ text(cm²)`  
`text(Side length)`  `= sqrt 49` 
`= 7\ text(cm)` 
`:.\ text(Volume)`  `= 7^3` 
`= 343\ text(cm³)` 
The flask pictured below can hold up to 100 mL of water.
How much water is in the flask?
`50\ text(mL)`  `70\ text(mL)`  `75\ text(mL)`  `80\ text(mL)` 




`text(75 mL)`
`text(Flask is fully filled until the 50 mL mark.)`
`text(Flask is half filled between 50 – 100 mL marks.)`
`:.\ text(Volume of water in the flask)`
`= 50 + 1/2 xx 50`
`= 75\ text(mL)`
Lily's backyard is in the shape of a rectangle and has an area of 30 m².
Kim's backyard is also rectangular but with side lengths that are triple those of Lily's backyard.
What is the area of Kim's backyard.
`10\ text(m²)`  `90\ text(m²)`  `120\ text(m²)`  `270\ text(m²)` 




`270\ text(m²)`
`text(Let the dimensions of Lily's backyard be:)\ \ x, y`
`text(Area) = xy = 30\ text(m²)`
`text(Kim's backyard is:)\ \ 3x xx 3y`
`text(Area)`  `= 3x xx 3y` 
`= 9xy`  
`= 9 xx 30\ text(m²)`  
`= 270\ text(m²)` 
Sequoia owns a farm with a rectangular paddock.
She increases the area of the paddock by adding land that changes it into the shape of a trapezium.
What is the area of Sequoia's new paddock, in square metres?
square metres 
`2599\ text(m²)`
`A`  `= 1/2h(a + b)` 
`= 1/2 xx 46 xx (42 + 71)`  
`= 2599\ text(m²)` 