Perimeter, Area and Volume Stage 3 - Short Problems

A collection of short Stage 3 problems on area and volume



Anulus Area

Stage: 3 and 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?

Regional Division

Stage: 3 and 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?

Televisual Technology

Stage: 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?

Hexa-split

Stage: 3 Short Challenge Level: Challenge Level:1

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

Guillotine

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

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

Pentagonal Area

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

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

L-emental

Stage: 3 Short Challenge Level: Challenge Level:1

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

Square in a Triangle

Stage: 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?

Square Ratio

Stage: 3 and 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?

Double Cover

Stage: 3 and 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?

3x3 Areas

Stage: 2 and 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?

Exactly Three-quarters

Stage: 3 and 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?

Hexagon Slices

Stage: 3 and 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?

Margins

Stage: 3 and 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?

Triangle in a Hexagon

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

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

Mid-point Area

Stage: 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?

Rectangle Cutting

Stage: 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?

Contact Circles

Stage: 3 Short Challenge Level: Challenge Level:1

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

Cover-up

Stage: 3 Short Challenge Level: Challenge Level:1

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: Challenge Level:2 Challenge Level:2

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: Challenge Level:1

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: 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?

3-sided

Stage: 3 and 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$^2$?

Gaudi's Design

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

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: Challenge Level:2 Challenge Level:2

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: Challenge Level:1

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: Challenge Level:2 Challenge Level:2

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