# 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.

### 3x3 Areas

##### KS 2 & 3 Short Challenge Level:

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

### 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?

### Televisual Technology

##### KS 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?

### 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?

### 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?

### Contact Circles

##### KS 3 Short Challenge Level:

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

### Cover-up

##### KS 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?

### L-emental

##### KS 3 Short Challenge Level:

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

### Square in a Triangle

##### KS 3 Short Challenge Level:

Weekly Problem 33 - 2006
A square is inscribed in an isoscles right angled triangle of area $x$. What is the area of the square?

### 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?

### Anulus Area

##### KS 3 & 4 Short 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?

### Margins

##### KS 3 & 4 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?

### Regional Division

##### KS 3 & 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?

### Square Ratio

##### KS 3 & 4 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?

### Double Cover

##### KS 3 & 4 Short Challenge Level:

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

### 3-sided

##### KS 3 & 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$^2$?

### Guillotine

##### KS 3 & 4 Short Challenge Level:

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

### Exactly Three-quarters

##### KS 3 & 4 Short Challenge Level:

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

### Pentagonal Area

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 18 - 2006
What is the area of the pentagon?

### Hexagon Slices

##### KS 3 & 4 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?

### Four Square

##### KS 3 & 4 Short Challenge Level:

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

### Cubic Masterpiece

##### KS 3 & 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?

### Sticky Fingers

##### KS 3 & 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?

### Gaudi's Design

##### KS 3 & 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?

### Emptied Cube

##### KS 4 Short Challenge Level:

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

### Trisected Triangle

##### KS 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?

### Cut-up Square

##### KS 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?