Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?
Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.
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.
Can you deduce the perimeters of the shapes from the information given?
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.
A task which depends on members of the group noticing the needs of others and responding.
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?
We started drawing some quadrilaterals - can you complete them?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
What happens to the area and volume of 2D and 3D shapes when you enlarge them?
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
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?
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. . . .
Can you find rectangles where the value of the area is the same as the value of the perimeter?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?