2. What is the area enclosed by the stage 2 squareflake? What about the stages 3 and 4 squareflakes?
3. If replacing each line segment on the edge with the zig-zag is […]
John plans to get the minimum possible Diamond Razor Mesh fencing material, as a security measure to discourage entry into his dam. He finds out that the rectangular shape drawn around the dam picture can help. The dimensions are given in algebraic form, in metres. Find an expression for the area of this […]
How many other triangles can you make with 11 sticks?
Investigate all the triangles that you can make with different numbers of sticks.
Record your […]
How many rectangles can you make with perimeter 12 units?
What do you know about rectangles? What is the smallest rectangle that you can […]
2. The rectangle is cut into two pieces along the dotted line and rearranged to make a triangle. Find the perimeter of the triangle.
The diagram shows a septagon ABCDEFG in which the lengths GA, AB, BC, CD, DE, EF are all equal and FG = 6 units. The area of the square BDFG is half the area of the septagon. Find the perimeter of the septagon.
Suppose another fence is built exactly one metre longer so the path between the two fences is the same width along the edges of the field. How wide would this path be?
Could a farmer drive […]
Suppose another fence is built exactly one metre longer so the path between the two fences is the same width all the way round including at the corners of the field.
How wide would this path be?
Would a mouse be able to run along it? […]
A wire belt is tied tightly around the Earth at the equator. Suppose the belt is made exactly one metre longer and held around the Earth at the equator so that it is the same distance away from the Earth everywhere. Would a mouse be able to crawl under the new belt? How do […]
Look at this square divided into four pieces : two identical triangles and two identical trapezia.
The edge of length 3 from each triangle matches with the edge of length 3 from a trapezium so that the four pieces from the square now occupy a rectangular space.
The square had side length […]