Can you find rectangles where the value of the area is the same as the value of the perimeter?
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?
What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?
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. . . .
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
A task which depends on members of the group noticing the needs of others and responding.
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
A tower of squares is built inside a right angled isosceles triangle. What fraction of the area of the triangle is covered by the squares?
If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage is the width decreased by ?
We started drawing some quadrilaterals - can you complete them?
Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?
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.
What happens to the area and volume of 2D and 3D shapes when you enlarge them?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?
Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make. . . .
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?