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Geometry Assessment Preparation

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Geometry Assessment Preparation

Arjun, Keira and Isla are planning a mountain hike in Aotearoa New Zealand. Solve each problem and show your working. Give units where needed. Use π = 3.14 unless a question says otherwise; round decimal answers to 1 decimal place.

Area and Scale

1.A trail information board is shaped like a parallelogram. Its base is 1.8 m and its perpendicular height is 0.75 m. What is its area?

2.A shelter roof panel is a trapezium with parallel sides 2.4 m and 3.6 m, and perpendicular height 1.5 m. Calculate its area.

3.A trail map uses a scale of 1:25,000. A section measures 7.2 cm on the map. How long is the real trail section in kilometres?

Angles and Triangles

4.At a trail junction, two parallel signposts are crossed by a straight path. One corresponding angle is 68°. What is the size of the other corresponding angle?

22°
68°
112°
180°

5.A triangular trail marker has two interior angles measuring 47° and 83°. Find the third angle and explain the angle fact you used.

6.A support cable forms a right-angled triangle with a 5 m horizontal distance and a 12 m vertical rise. How long is the cable?

7.A lookout platform is a regular hexagon. Calculate the sum of its interior angles, then find each interior angle.

Solid Geometry and Units

8.A cylindrical water container has radius 0.4 m and height 1.2 m. Find its volume in cubic metres and in litres. (1 m³ = 1,000 L.)

9.Keira estimates that 2.5 m² is 250 cm². Is she correct? Convert 2.5 m² to cm² and explain the conversion.

10.A rectangular equipment crate is 0.5 m long, 0.4 m wide and 0.3 m high. Calculate its volume in m³. If all three dimensions are doubled, by what factor does the volume change?