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Composite Shapes and Perimeter

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Composite Shapes and Perimeter

A community group is planning a dog park from connected rectangular zones. Perimeter is the distance around the outside edge. Use the dimensions given to solve each challenge. Show your working and include units.

Trace the outside edge

The longer rectangle measures 8 m by 3 m. A smaller rectangle measuring 4 m by 3 m is attached along its full 3 m side to the middle of the longer rectangle’s 8 m side.

1.Find the perimeter of the combined shape. Add the outside edges only; do not count the shared edge.

2.Which statement explains why the shared edge is not counted in the perimeter?

It is inside the combined shape, not on its outside boundary.
It is shorter than the other sides.
Shared edges are always zero metres.
It belongs to both rectangles, so count it twice.

Solve the garden-bed puzzle

A rectangular garden bed is 12 m wide and 8 m high, with a rectangular notch cut into its top edge. The notch is 4 m wide and 3 m deep, leaving two 4 m top ledges. Use these dimensions to work out the perimeter.

3.Add the outside edges using the dimensions given for the U-shaped bed. What is its perimeter?

4.A new U-shaped bed has overall width 15 m. Its two top ledges are 5 m and 4 m long. How wide is the notch between them?

5.The outside height of that bed is 9 m and the notch is 2 m deep. What is the total length of its vertical boundary edges?

Plan, check and explain

Use perimeter reasoning to help the park team make practical decisions.

6.A rectangular dog-run is 10 m by 6 m. A 4 m by 2 m rectangle is joined along one of its 2 m sides to an outside edge of the dog-run. Find the perimeter of the new shape.

7.The park has 50 m of fencing. A play area needs 18 m of fencing along three sides because its fourth side is an existing wall. How much fencing remains for another enclosure?

8.True or false: If a shape is split into two rectangles for working out, adding both complete perimeters always gives the perimeter of the combined shape.

TrueFalse

9.Draw a composite rectilinear shape made from two rectangles joined along a full side. Label every outside side so its perimeter is exactly 28 m. Show one way to check your total.

10.In one or two sentences, explain a reliable method for finding the perimeter of a composite shape when some side lengths are missing.