Area Stage 3 - Short Problems

A collection of short Stage 3 problems on area and volume



Weekly Problem 36 - 2011

Challenge Level: Challenge Level:1

Imagine cutting out a circle which is just contained inside a semicircle. What fraction of the semi-circle will remain?

Weekly Problem 38 - 2011

Challenge Level: Challenge Level:1

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

Weekly Problem 52 - 2011

Challenge Level: Challenge Level:1

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

Weekly Problem 16 - 2008

Stage: 3 and 4 Challenge Level: Challenge Level:1

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?

Weekly Problem 30 - 2009

Stage: 3 Short Challenge Level: Challenge Level:1

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: Challenge Level:1

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?

Weekly Problem 8 - 2010

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Are you able to find triangles such that these five statements are true?

Weekly Problem 25 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

These four touching circles have another circle hiding amongst them...

Weekly Problem 49 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

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?

Weekly Problem 7 - 2011

Stage: 3 and 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

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

Weekly Problem 33 - 2014

Stage: 3 Challenge Level: Challenge Level:1

Weekly Problem 33 - 2014

Weekly Problem 49 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 49 - 2014

Weekly Problem 11 - 2016

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Four cubes are placed together to make a cuboid. What is the surface area of this cuboid?

Weekly Problem 23 - 2016

Stage: 3 Short Challenge Level: Challenge Level:1

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?

Weekly Problem 26 - 2016

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

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?

Weekly Problem 33 - 2016

Stage: 3 Short Challenge Level: Challenge Level:1

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?

Weekly Problem 35 - 2016

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

What is the total perimeter of the squares, if the line GH in the diagram is 24cm?

Weekly Problem 43 - 2016

Stage: 3 Short Challenge Level: Challenge Level:1

In the diagram, the small squares are all the same size. What fraction of the large square is shaded?

Weekly Problem 50 - 2016

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

A large cuboid is made from cubes of equal size. What fraction of the surface area of the large cuboid is black?