Resources tagged with: Area - squares and rectangles

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Broad Topics > Measuring and calculating with units > Area - squares and rectangles

Semi-detached

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.

Compare Areas

Age 14 to 16 Challenge Level:

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

Take a Square

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.

From One Shape to Another

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.

Poly Plug Rectangles

Age 5 to 14 Challenge Level:

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Changing Areas, Changing Perimeters

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?

Making Rectangles

Age 7 to 14 Challenge Level:

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

Tilted Squares

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?

Perimeter Challenge

Age 11 to 14 Challenge Level:

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

Framed

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. . . .

The Square Under the Hypotenuse

Age 14 to 16 Challenge Level:

Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

Growing Rectangles

Age 11 to 14 Challenge Level:

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

Can They Be Equal?

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?

Completing Quadrilaterals

Age 11 to 14 Challenge Level:

We started drawing some quadrilaterals - can you complete them?

Perimeter Possibilities

Age 11 to 14 Challenge Level:

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

Warmsnug Double Glazing

Age 14 to 16 Challenge Level:

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

Fence It

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?

Alison's Quilt

Age 11 to 14 Challenge Level:

Nine squares are fitted together to form a rectangle. Can you find its dimensions?

Place Your Orders

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?