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

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.

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.

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!

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?

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. . . .

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?

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

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

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?

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

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

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

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?

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