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Framed
Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of the pictures.
Tilted Squares
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Four or Five
The diagram shows a large rectangle composed of 9 smaller rectangles. If each of these rectangles has integer sides, what could the area of the large rectangle be?
Age 11 to 14
Challenge Level
Find the dimensions of the following rectangles:
| Dimensions | Area | Perimeter |
| 9 | 20 | |
| 16 | 20 | |
| 21 | 20 | |
| 24 | 20 | |
| 25 | 20 |
Draw the rectangles.
What do you notice about the shapes of rectangles with a fixed perimeter as their areas increase?
Find the dimensions of the following rectangles:
| Dimensions | Area | Perimeter |
| 24 | 20 | |
| 24 | 22 | |
| 24 | 28 | |
| 24 | 50 |
Draw the rectangles.
What do you notice about the shapes of rectangles with a fixed area as their perimeters increase?
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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.