Work Out Missing Lengths of Multi-Rectangular Shapes

Look at this shape which is made of two rectangles joined together.

There is a 6 cm by 2 cm rectangle lying flat and a 3 cm by 7 cm rectangle lying upright.

We can use the fact that rectangles have parallel sides of equal length to work out missing distances in rectangular arrangements.

Example 1

In the diagram above, work out the length a in cm.

Answer

Use the fact that the top rectangle is 2 cm tall all the way along, even at its right-hand edge.

Also the upright rectangle is 7 cm tall even at its left-hand edge.

This is shown in the diagram below.

This means that a is 7 cm - 2 cm = 5 cm.

Example 2

In the diagram, work out the length a in cm.

Answer

Use the fact that the top of the blue rectangle will match the length of the bottom as 4 cm.

The length a will be 7 cm + 4 cm.

This is shown in the diagram below.

This means that a is 7 cm + 4 cm = 11 cm.

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