Perimeter and Area of Composite Shapes

Solve problems involving the area and perimeter of irregular and composite shapes using appropriate units.

Split the shape into pieces you already know. Then decide whether to add the pieces or subtract one from another.

Method

Split or subtract

Either cut the shape into known parts, or take a piece out of a bigger rectangle.

Perimeter is the outside only

Cut lines you draw are not part of the perimeter. This is the classic error.

Find missing sides by matching

Opposite sides of the whole shape must balance.

Label every piece before calculating

It stops you counting a side twice or missing one.

e.g.

\text{An L-shape is a } 10 \times 6 \text{ rectangle with a } 4 \times 3 \text{ corner removed. Find its area and perimeter.}

Choose a method. Here, subtracting is easier than splitting. $\text{big rectangle} - \text{corner}$
Find the area of the whole rectangle. $10 \times 6 = 60$
Find the area of the removed corner. $4 \times 3 = 12$
Subtract for the area. $60 - 12 = 48 \text{ units}^2$
For the perimeter, walk around the outside and add every edge. $10 + 6 + 6 + 3 + 4 + 3 = 32$
Note the cut line is not counted. It is inside the shape. $P = 32 \text{ units}$

Walk the outside for perimeter. Split or subtract for area.

\text{A } 8\times5 \text{ rectangle with a } 2\times2 \text{ square removed. Area?}

Answer

40 - 4 = 36

\text{Two rectangles } 6\times2 \text{ and } 4\times3 \text{ joined. Total area?}

Answer

12 + 12 = 24

\text{Why is the join line not part of the perimeter?}

Answer

\text{It is inside the shape, not on the outside.}

\text{An L-shape has outer sides } 9,4,5,2,4,2. \text{ Find the perimeter.}

Answer

26

\text{A square of side 10 has a } 3\times3 \text{ hole. Area?}

Answer

100 - 9 = 91

\text{Which is easier for a shape with a bite out: splitting or subtracting?}

Answer

\text{Subtracting.}