### There are 18 results

Broad Topics >

Measuring and calculating with units > Area - squares and rectangles

##### Age 14 to 16 Challenge Level:

Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?

##### Age 7 to 14

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.

##### Age 14 to 16 Challenge Level:

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.

##### Age 11 to 14 Challenge Level:

Can you deduce the perimeters of the shapes from the information given?

##### Age 14 to 16 Challenge Level:

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 7 to 14 Challenge Level:

A task which depends on members of the group noticing the needs of others and responding.

##### Age 11 to 14 Challenge Level:

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?

##### Age 11 to 14 Challenge Level:

We started drawing some quadrilaterals - can you complete them?

##### Age 11 to 14 Challenge Level:

It's easy to work out the areas of most squares that we meet, but
what if they were tilted?

##### Age 11 to 14 Challenge Level:

What happens to the area and volume of 2D and 3D shapes when you
enlarge them?

##### Age 11 to 14 Challenge Level:

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

##### Age 11 to 14 Challenge Level:

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

##### Age 11 to 14 Challenge Level:

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

##### Age 11 to 14 Challenge Level:

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?

##### Age 11 to 14 Challenge Level:

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. . . .

##### Age 11 to 14 Challenge Level:

Can you find rectangles where the value of the area is the same as the value of the perimeter?

##### Age 11 to 14 Challenge Level:

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

##### Age 7 to 14 Challenge Level:

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?