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Compare Areas
Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?
Take a Square
Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.
Semi-detached
A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
Age 14 to 16
Challenge Level
Start by looking at the windows with only one pane.
Are there any windows that use the same amount of glass?
How do their frame lengths differ?
Are there any windows that use the same amount of frame?
How do their glass areas differ?
Click to reveal a handy table with the areas and frame lengths of all the windows:
| Length of frame |
Area | Cost | |
| A | 28 | 32 | £880 |
| B | 16 | 15 | £470 |
| C | 12 | 8 | £320 |
| D | 20 | 16 | £560 |
| E | 18 | 12 | £550 |
| F | 12 | 9 | £330 |
| G | 26 | 24 | £760 |
| H | 8 | 3 | £190 |
| I | 14 | 12 | £400 |
| J | 8 | 4 | £200 |
| K | 17 | 12 | £460 |
| L | 23 | 20 | £660 |
| M | 24 | 36 | £840 |
| N | 20 | 24 | £640 |
| O | 16 | 12 | £440 |
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.