**"Perimeter"**

## Years 9 – 12 Surprise Ratios

*By toni On 3 May, 2020 · Leave a Comment*

A circle of radius r and centre O, is inscribed in a triangle with edges of lengths a, b and c.

Find the area and circumference of the circle.

Find the area and the perimeter of the triangle.

What do you notice about the ratios of the two areas and the ratios […]

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 8 […]

## Years 7 – 12 Squareflake Fractal

*By toni On 14 September, 2019 · Leave a Comment*

1. If the red square has area 1 square unit. What is the area enclosed by the stage 1 squareflake?

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 […]

## Years 10 – 12 Quadratic Equations

*By Kwethemba Moyo On 14 September, 2019 · Leave a Comment*

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 […]

## Grades 4 to 8 Making Triangles

*By toni On 12 November, 2017 · Leave a Comment*

Use 11 sticks of equal length to make this triangle with edge lengths 2, 4 and 5. You might like to record this as (2, 4, 5).

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 […]

## Years 5 – 8 Wholesome Rectangles

*By toni On 15 October, 2017 · Leave a Comment*

This activity is about rectangles with whole number dimensions. With other lengths and breadths there are infinitely many possible rectangles so here we just stick to whole numbers.

How many rectangles can you make with perimeter 12 units?

What do you know about rectangles? What is the smallest rectangle that you can […]

## Years 8 – 11 Riding on Pythagoras 1

*By toni On 3 November, 2016 · Leave a Comment*

1. Find the area of the quadrilateral.

2. The rectangle is cut into two pieces along the dotted line and rearranged to make a triangle. Find the perimeter of the triangle.

## Years 8 – 11 Riding on Pythagoras 2

*By toni On 3 November, 2016 · Leave a Comment*

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.

## Years 6 – 9 Square Fence

*By toni On 23 March, 2013 · 7 Comments*

A fence is built around a square field.

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?

Would a mouse be able to run along it?

Could a farmer drive […]

## Years 8 – 12 Not-So-Square Fence

*By toni On 22 March, 2013 · 5 Comments*

A fence is built around a square field.

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? […]

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