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Geometry Problem Solving Workshop
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Geometry Problem Solving Workshop
A design team is planning a mini adventure park. Solve each geometry challenge, show your working, and include units where needed. Diagrams are not drawn to scale.
Angles and clues
Use angle rules to decode the park’s layout.
1.At a triangular sign, two interior angles are 38° and 67°. Find the third angle and name the angle fact you used.
2.A four-sided paved area is a parallelogram. One interior angle is 112°. Work out the other three interior angles.
3.Two straight paths cross. One angle is 47°. Find the other three angles around the intersection, explaining which angles are equal and which add to 180°.
Measure and scale
Plan a route and check the dimensions before building.
4.A rectangular lawn is 9 m long and 12 m wide. A straight path runs from one corner to the opposite corner. Use Pythagoras’ theorem to find the path length.
5.On a scale plan, 1 cm represents 2.5 m. A path measures 7.2 cm on the plan. What is its actual length?
6.A triangular shade sail has a base of 8 m and a perpendicular height of 3.5 m. Find its area. Then find the area of a similar sail with every length enlarged by a scale factor of 1.5.
Reason it out
Explain why a tempting claim may or may not be true.
7.A designer claims that each interior angle of a regular hexagonal platform is 120°. Is the claim correct? Justify your answer using the interior-angle sum formula (n − 2) × 180° and the fact that all six angles are equal.
8.A designer says every rectangle is a square because both have four right angles. Is the claim correct? Use a defining property or a counterexample to justify your answer.
9.A ramp rises 1.2 m over a horizontal distance of 5 m. Calculate the ramp’s length to 2 decimal places. State why the ramp length is not 5 m.
10.Create a short geometry challenge for another park designer that needs two different geometry rules to solve. Write the problem and its full solution.
3 printable pages
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