MathsFreePrintable
Shapes and Problem Solving
A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.
Name:Date:
Shapes and Problem Solving
Use shape properties, perimeter and area to help plan a garden and solve each challenge. Show your working and include units. Use π ≈ 3.14 where needed.
Shape detectives
Identify useful properties before you calculate.
1.A regular octagonal planter has a perimeter of 72 cm. What is the length of each equal side?
2.A rhombus-shaped sign is being considered for the garden entrance. Which two statements must be true of every rhombus? Choose two.
- All four sides are equal in length.
- All four angles are right angles.
- Both pairs of opposite sides are parallel.
- Its diagonals are always equal in length.
3.A circular herb bed has a radius of 3 m. Estimate its area to the nearest square metre using π ≈ 3.14. Include the calculation.
Plan and calculate
Use measurements and geometric reasoning to make the garden work.
4.A triangular shade sail has a base of 2.4 m and a perpendicular height of 1.5 m. What is its area?
5.A rectangular pond is 8 m long and 5 m wide. A path 1 m wide will go all the way around the outside. What area will the pond and path cover altogether?
6.A 12 m by 9 m rectangular lawn has a 3 m by 2 m flower bed cut out of one corner. What area of lawn remains? Sketch the large rectangle and the cut-out to show your method.
7.A square compost area has sides of 4 m. How many metres of edging are needed to go all the way around it? If edging is sold in 5 m rolls, how many rolls must be bought?
8.Jarrah says, “If I double both side lengths of a rectangle, its area only doubles.” Is she correct? Use a rectangle measuring 6 cm by 4 cm to explain what happens to its area when both dimensions are doubled.
9.A trapezium-shaped vegetable patch has parallel sides of 10 m and 6 m, and a perpendicular height of 4 m. Calculate its area using A = ½ × (sum of parallel sides) × height.
10.The garden team has 48 m of fencing for a rectangular enclosure. One side must be 16 m long. What must the other side measure? Explain how you know.
2 printable pages
Page 1
Page 2
About This Worksheet
Free in Kuraplan
Sign up free, grab the PDF, and customize it for your class.
Print-Ready
Formatted for standard paper. Clean layout, easy to read.
AI-Generated
Created with Kuraplan's AI, designed for real classroom use.
For Teachers & Parents
Use in classrooms, for homework, tutoring, or homeschool.
Need a custom version of this worksheet?
Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.
Generate Custom Worksheets — Free No credit card Curriculum-aligned Under 60 seconds
