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:

Challenge Level:1

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:

Challenge Level:1

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?

Televisual Technology

KS 3 Short Challenge Level:

Challenge Level:1

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?

Rectangle Cutting

KS 3 Short Challenge Level:

Challenge Level:1

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?

Hexa-split

KS 3 Short Challenge Level:

Challenge Level:1

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

Contact Circles

KS 3 Short Challenge Level:

Challenge Level:1

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

L-emental

KS 3 Short Challenge Level:

Challenge Level:1

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

Shaded End

KS 3 Short Challenge Level:

Challenge Level:1

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

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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?

Sideways Ratio

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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?

Square in a Triangle

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Cover-up

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

Annulus Area

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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?

Square Ratio

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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?

3-sided

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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$^2$?

Regional Division

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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?

Double Cover

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Four Square

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Open the Box

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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?

Exactly Three-quarters

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Guillotine

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Hexagon Slices

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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 Cubes

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Margins

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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?

Cubic Masterpiece

KS 3 & 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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?

Pile Driver

KS 3 & 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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