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Geometry Problem Solving Workshop

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Geometry Problem Solving Workshop

Solve each problem and show your working. Give units where needed. Use π = 3.14 unless a question says otherwise.

Angles and polygons

The team is helping prepare the tournament court.

1.At a court corner, two sides meet to form a triangle-shaped support. Its angles are 38° and 67°. Find the third angle and state the angle rule you used.

2.The centre-circle marking is a regular hexagon in a practice layout. Calculate the size of each interior angle. Show how the sum of the interior angles leads to your answer.

3.A practice court is drawn as a rectangle 30 m long and 15 m wide. What is its perimeter? Explain why you add each dimension twice.

4.A regular polygon sign has an exterior angle of 45° at each vertex. How many sides does the sign have? Show the relationship you use.

Similarity and scale

The team is using a scale drawing to plan court equipment and markings.

5.On a scale plan, a 30 m court is 12 cm long. A practice area is 9 cm wide on the same plan. How wide is the real practice area? Include units.

6.Two similar triangular pennants have corresponding side lengths in the ratio 3:5 (small to large). The small pennant has a perimeter of 24 cm. Find the large pennant's perimeter.

7.Ari stands 1.6 m tall and casts a 2 m shadow. At the same time, a goal post casts a 7.5 m shadow. Assuming the ground is level and the sun's rays make matching angles, find the goal post's height.

Area, circles and reasoning

Use geometric rules to check whether the tournament set-up will fit.

8.A rectangular warm-up zone measures 18 m by 10 m. A 1 m-wide safety strip is added all the way around the outside. Find the total area, including the strip, and then find the area of the strip alone.

9.A circular training target has radius 4.5 m. Calculate its circumference to the nearest tenth of a metre. Use C = 2πr and π = 3.14.

10.A quadrilateral on the tournament plan has angles of 85°, 92° and 108°. Work out the fourth angle and name the rule that confirms your result.

11.The centres of two circular practice targets are 10 cm apart. Their radii are 3 cm and 5 cm. Do the circles overlap, touch externally, or stay separate? Justify by comparing the centre distance with the sum of the radii.