# Perimeter, Area and Volume Stage 3 - Short Problems

### Anulus Area

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 38 - 2011
Given three concentric circles, shade in the annulus formed by the smaller two. What percentage of the larger circle is now shaded?

### Regional Division

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 52 - 2011
Draw two intersecting rectangles on a sheet of paper. How many regions are enclosed? Can you find the largest number of regions possible?

### Televisual Technology

##### Stage: 3 Short Challenge Level:

Weekly Problem 27 - 2012
Television screens have changed from the traditional 4:3 to widescreen 16:9. If a new television and an old television have the same area, what is the ratio of their widths?

### Hexa-split

##### Stage: 3 Short Challenge Level:

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

### Weekly Problem 16 - 2008

##### Stage: 3 and 4 Challenge Level:

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?

### Triangle in a Hexagon

##### Stage: 3 Short Challenge Level:

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

### Weekly Problem 30 - 2009

##### Stage: 3 Short Challenge Level:

M is the midpoint of the side of the rectangle. What is the area (in square units) of the triangle PMR?

### Weekly Problem 50 - 2009

##### Stage: 3 Short Challenge Level:

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?

### Contact Circles

##### Stage: 3 Short Challenge Level:

Weekly Problem 25 - 2010
These four touching circles have another circle hiding amongst them...

### Cover-up

##### Stage: 3 Short Challenge Level:

Weekly Problem 49 - 2010
When I place a triangle over a small square, or cover a larger square with the same triangle, a certain proportion of each is covered. What is the area of the triangle?

### Sticky Fingers

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 7 - 2011
Roo wants to puts stickers on the cuboid he has made from little cubes. Will he have any stickers left over?

### Sideways Ratio

##### Stage: 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

##### Stage: 3 and 4 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?

### 3-sided

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 9 - 2015
How many triangles can Jack draw with two sides of lengths $6$cm and $8$cm and an area of $7$cm$^2$?

### Gaudi's Design

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 12 - 2015
Eight lines are drawn in a regular octagon to form a pattern. What fraction of the octagon is shaded?

### Cut-up Square

##### Stage: 4 Short Challenge Level:

Weekly Problem 15 - 2015
In the diagram, two lines have been draawn in a square. What is the ratio of the areas marked?

### Four Square

##### Stage: 3 and 4 Short Challenge Level:

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

### Emptied Cube

##### Stage: 4 Short Challenge Level:

Weekly Problem 26 - 2015
What are the volume and surface area of this 'Cubo Vazado' or 'Emptied Cube'?

### Trisected Triangle

##### Stage: 4 Short Challenge Level:

Weekly Problem 34 - 2015
Four tiles are given. For which of them can three be placed together to form an equilateral triangle?

### Open the Box

##### Stage: 3 and 4 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

##### Stage: 3 and 4 Short Challenge Level:

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

### Four Cubes

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 11 - 2016
Four cubes are placed together to make a cuboid. What is the surface area of this cuboid?

##### Stage: 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?

### Cubes on a Cube

##### Stage: 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?

### Six Circles

##### Stage: 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?

### Line of Squares

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 35 - 2016
What is the total perimeter of the squares, if the line GH in the diagram is 24cm?

### Squares in a Square

##### Stage: 3 Short Challenge Level:

Weekly Problem 43 - 2016
In the diagram, the small squares are all the same size. What fraction of the large square is shaded?

### Chequered Cuboid

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 50 - 2016
A large cuboid is made from cubes of equal size. What fraction of the surface area of the large cuboid is black?

### Star in a Hexagon

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 20 - 2017
The diagram shows a design formed by drawing six lines in a regular hexagon. What fraction of the hexagon is shaded?

### Strawberries and Peas

##### Stage: 3 Short Challenge Level:

Weekly Problem 17 - 2017
Yasmin has beds for peas and strawberries in her rectangular garden. She lengthened one side of her pea bed by 3m to make it a square. This reduced her strawberry patch by 15m^2. What was the original area of her pea bed?

### Corner Cut

##### Stage: 3 Short Challenge Level:

Weekly Problem 23 - 2017
Three small equilateral triangles of the same size are cut from the corners of a larger equilateral triangle. What is the side length of the small triangles?

### Leaning Over

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 31 - 2017
The triangle HIJ has the same area as the square FGHI. What is the distance from J to the line extended through F and G?

### Soma Surface

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 48 - 2017
What is the surface area of the solid shown?

### Christmas Cut-out

##### Stage: 3 Short Challenge Level:

Weekly Problem 52 - 2017
Sue cuts some squares from a piece of paper to make a Christmas decoration. What is the perimeter of the resulting shape?