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Irregular Shape Area Decomposition
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Irregular Shape Area Decomposition
Help plan a new community garden by splitting irregular shapes into familiar ones. Use square units where appropriate, show your working, and remember: area is measured in square units.
Choose a useful strategy
1.A garden bed is L-shaped. Which plan is a sensible way to find its area?
- Split it into two non-overlapping rectangles, find each area, then add them.
- Measure only the longest side and multiply by itself.
- Split it into two circles and add their areas.
- Add all the side lengths together.
2.A rectangular planter is 7 m long and 3 m wide. Calculate its area and include the correct units.
3.A triangular flower bed has a base of 8 m and a perpendicular height of 5 m. Find its area.
Split it and solve it
4.A paved seating area is made from two rectangles that meet edge to edge. Rectangle A is 6 m by 4 m. Rectangle B is 3 m by 2 m. What is the total area?
5.An L-shaped lawn can be seen as a 10 m by 8 m rectangle with a 4 m by 3 m rectangle cut out of one corner. Calculate the lawn area.
6.A garden design is a 9 m by 5 m rectangle with a triangular section added along one side. The triangle has base 5 m and perpendicular height 4 m. Find the total area.
7.True or false? When you split a shape into parts to find its area, the parts must not overlap.
TrueFalse
8.A composite shape is split into a 5 cm by 4 cm rectangle and a triangle with base 5 cm and height 3 cm. Complete the calculation: total area = (5 × 4) + (½ × 5 × 3) = cm².
9.Make your own composite garden bed from at least two familiar shapes. Sketch it, label the measurements you choose, and calculate its total area. Make sure the sections do not overlap.
10.A small deck has an area of 42 m². One rectangular section is 6 m by 5 m. The deck is made from that section and one more rectangle attached without overlap. What area must the second rectangle have? Give one possible set of whole-number dimensions for it.
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