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

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

How would you move the bands on the pegboard to alter these shapes?

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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?

This interactivity allows you to sort logic blocks by dragging their images.

Can you each work out what shape you have part of on your card? What will the rest of it look like?

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

This activity challenges you to make collections of shapes. Can you give your collection a name?

Find out what a "fault-free" rectangle is and try to make some of your own.

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

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. . . .

Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

An AP rectangle is one whose area is numerically equal to its perimeter. If you are given the length of a side can you always find an AP rectangle with one side the given length?

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

Is the sum of the squares of two opposite sloping edges of a rectangular based pyramid equal to the sum of the squares of the other two sloping edges?

X is a moveable point on the hypotenuse, and P and Q are the feet of the perpendiculars from X to the sides of a right angled triangle. What position of X makes the length of PQ a minimum?

A hallway floor is tiled and each tile is one foot square. Given that the number of tiles around the perimeter is EXACTLY half the total number of tiles, find the possible dimensions of the hallway.

An activity making various patterns with 2 x 1 rectangular tiles.

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

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?