# Perimeter, Area and Volume Stage 3 - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Perimeter, Area and Volume - Stage 3.

Printable worksheets containing selections of these problems are available here:

 Stage 3 ★ Sheet 1 Solutions Stage 3 ★★ Sheet 1 Solutions Stage 3 ★★★ Sheet 1 Solutions Sheet 2 Solutions

### Hexa-split

##### KS 3 Short Challenge Level:

Weekly Problem 39 - 2013
Which of the areas shown in the hexagons are equal to each other?

### Rectangle Cutting

##### KS 3 Short Challenge Level:

Weekly Problem 50 - 2009
Tom and Jerry start with identical sheets of paper. Each one cuts his sheet in a different way. Can you find the perimeter of the original sheet?

##### KS 3 Short Challenge Level:

Weekly Problem 23 - 2016
The diagram shows a cuboid in which the area of the shaded face is one quarter of the area of each of the two visible unshaded faces. What is the area of one of the unshaded faces?

### Six Circles

##### KS 3 Short Challenge Level:

Weekly Problem 33 - 2016
In the diagram, six circles of equal size touch adjacent circles and the sides of the large rectangle. What is the perimeter of the large rectangle?

### Square Ratio

##### KS 3 Short Challenge Level:

Weekly Problem 52 - 2006
A square is divided into four rectangles and a square. Can you work out the ratio of the side lengths of the rectangles?

### 3x3 Areas

##### KS 3 Short Challenge Level:

Weekly Problem 24 - 2007
Which of the following shaded regions has an area different from the other shaded regions?

### Mid-point Area

##### KS 3 Short Challenge Level:

Weekly Problem 30 - 2009
M is the midpoint of the side of the rectangle. What is the area (in square units) of the triangle PMR?

### Exactly Three-quarters

##### KS 3 Short Challenge Level:

Weekly Problem 30 - 2007
Three-quarters of the area of the rectangle has been shaded. What is the length of x?

### Guillotine

##### KS 3 Short Challenge Level:

Weekly Problem 9 - 2006
What fraction of the area of the rectangle is shaded?

### Intersecting Squares

##### KS 3 Short Challenge Level:

Weekly Problem 32 - 2014
Three overlapping squares are shown. If you know the areas of the overlapping and non-overlapping parts, can you work out the side lengths of the squares?

### Margins

##### KS 3 Short Challenge Level:

Weekly Problem 16 - 2008
A 30cm x 40cm page of a book includes a 2cm margin on each side... What percentage of the page is occupied by the margins?

### Cubes on a Cube

##### KS 3 Short Challenge Level:

Weekly Problem 26 - 2016
A cube has each of its faces covered by one face of an identical cube, making a solid as shown. What is the surface area of the solid?

### L-emental

##### KS 3 Short Challenge Level:

Weekly Problem 28 - 2006
What can you say about the rectangles that form this L-shape?

### Sideways Ratio

##### KS 3 Short Challenge Level:

Weekly Problem 33 - 2014
A rectangle with area $125\text{cm}^2$ has sides in the ratio $4:5$. What is the perimeter of the rectangle?

### Cubic Masterpiece

##### KS 3 Short Challenge Level:

Weekly Problem 49 - 2014
A solid wooden cube is painted blue on the outside. The cube is then cut into 27 smaller cubes of equal size. What fraction of the total surface area of these new cubes is blue?

### Tangram Area

##### KS 3 Short Challenge Level:

Weekly Problem 29 - 2008
The seven pieces in this 12 cm by 12 cm square make a Tangram set. What is the area of the shaded parallelogram?

### Double Cover

##### KS 3 Short Challenge Level:

Weekly Problem 3 - 2007
What is the ratio of the area of the table covered twice, to the uncovered area?

### Triangles' Triangle

##### KS 3 Short Challenge Level:

Weekly Problem 27 - 2009
The perimeter of a large triangle is 24 cm. What is the total length of the black lines used to draw the figure?

### Open the Box

##### KS 3 Short Challenge Level:

Weekly Problem 37 - 2015
A piece of card is folded to make an open box. Given its surface area, can you work out its volume?

### Pile Driver

##### KS 3 Short Challenge Level:

Weekly Problem 38 - 2015
Where does the line through P that halves the figure shown meet the edge XY?

### Hexagon Slices

##### KS 3 Short Challenge Level:

Weekly Problem 37 - 2007
This regular hexagon has been divided into four trapezia and one hexagon.... what is the ratio of the lengths of sides p, q and r?

### Triangle in a Hexagon

##### KS 3 Short Challenge Level:

Weekly Problem 3 - 2009
What fraction of the area of this regular hexagon is the shaded triangle?

### Four Square

##### KS 3 Short Challenge Level:

Weekly Problem 17 - 2015
A square contains two overlapping squares. What is the total of the shaded regions?