Geometry and Measurement Diagnostic

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📐 Part 1: Area, Perimeter & Circles

1. A rectangle has a length of 12 cm and a width of 7 cm. Calculate its perimeter and area.

Perimeter = _______________ Area = _______________

2. A composite shape is made up of a 10 m × 6 m rectangle with a 3 m × 3 m square cut from one corner. Calculate the area of the composite shape.

3. A circle has a radius of 5 cm. Calculate its circumference and area. (Use π = 3.14)

Circumference = _______________ Area = _______________

4. Which formula is used to find the area of a circle? Circle your answer.

A = 2πr

A = πr²

A = πd

A = 2πr²

📏 Part 2: Pythagoras, 3D Shapes & Scale

5. A right-angled triangle has legs of 6 cm and 8 cm. Use Pythagoras' Theorem to find the length of the hypotenuse.

6. A ladder leans against a wall. The base of the ladder is 2.4 m from the wall and the ladder reaches 3.2 m up the wall. How long is the ladder?

7. A rectangular prism (box) has length 8 cm, width 5 cm, and height 3 cm.

(a) Calculate the volume: _______________

(b) Calculate the surface area: _______________

8. A map has a scale of 1 : 50 000. Two towns are 6 cm apart on the map. What is the actual distance between the towns in kilometres?

9. A shape is enlarged by a scale factor of 3. The original shape has an area of 12 cm². What is the area of the enlarged shape? (Hint: area scale factor = k²)

🚗 Part 3: Speed, Distance & Time

10. A car travels 240 km in 3 hours. What is its average speed?

Speed = _______________ km/h

11. A cyclist rides at 18 km/h for 45 minutes. How far do they travel?

12. Problem Solving: Aroha drives from Auckland to Hamilton (128 km) at 80 km/h, then from Hamilton to Tauranga (86 km) at 100 km/h. What is her total travel time? Give your answer in hours and minutes.