Year 7 Measurement: free practice test with answers

Sample measurement questions with answers

Try each one before you open the answer.

1. Metric units of length

   Convert:

   (a) $4.7$ km to metres (b) $365$ cm to metres

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   Key idea: $1$ km $= 1000$ m and $1$ m $= 100$ cm. Multiply to go to a smaller unit, divide to go to a larger unit.

   1. (a) $4.7 \times 1000 = 4700$ m
   2. (b) $365 \div 100 = 3.65$ m

   Answer: (a) $4700$ m (b) $3.65$ m

2. Perimeter

   Find the perimeter of a rectangle that is $14$ cm long and $9$ cm wide.

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   Key idea: Perimeter of a rectangle $= 2 \times \text{length} + 2 \times \text{width}$.

   1. $2 \times 14 + 2 \times 9 = 28 + 18 = 46$ cm

   Answer: $46$ cm

3. Arc length and perimeter of sectors and composite shapes

   A sector is a quarter of a circle with radius $8$ m.

   (a) Find the exact length of its arc, in terms of $\pi$.

   (b) Find its perimeter, using $\pi \approx 3.14$.

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   Key idea: The arc of a quarter circle is $\dfrac{1}{4}$ of the circumference $2\pi r$. The perimeter of a sector is the arc plus two radii.

   1. (a) Arc $= \dfrac{1}{4} \times 2 \times \pi \times 8 = 4\pi$ m
   2. (b) $4\pi \approx 4 \times 3.14 = 12.56$ m
   3. (b) Perimeter $= 12.56 + 8 + 8 = 28.56$ m

   Answer: (a) $4\pi$ m (b) $28.56$ m

4. Units of area and area of rectangles

   A rectangular room is 7 m long and 4 m wide. What is the area of the room in square metres?

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   Key idea: Area of a rectangle = length × width

   1. Write the formula: $A = l \times w$
   2. Substitute the values: $A = 7 \times 4$
   3. Calculate: $A = 28$

   Answer: $28 \text{ m}^2$

5. Area of triangles

   Find the area of a triangle with a base of $8$ cm and a perpendicular height of $5$ cm.

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   Key idea: The area of a triangle is $A = \dfrac{1}{2} \times b \times h$, where $b$ is the base and $h$ is the perpendicular height.

   1. Write the formula: $A = \frac{1}{2} \times b \times h$
   2. Substitute $b = 8$ and $h = 5$: $A = \frac{1}{2} \times 8 \times 5$
   3. Calculate: $A = \frac{1}{2} \times 40 = 20$

   Answer: The area of the triangle is $20$ cm².

6. Area of composite shapes

   A compound shape is made by joining a rectangle and a square. The rectangle is $10$ m long and $4$ m wide. The square has a side length of $4$ m and is attached to the right end of the rectangle, so the two shapes share one $4$ m edge. Find the total perimeter and total area of the compound shape.

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   Key idea: For a compound shape, split it into simpler shapes to find the area, and trace the outside edges carefully to find the perimeter.

   1. Find the area of the rectangle: $A_{\text{rect}} = 10 \times 4 = 40 \text{ m}^2$
   2. Find the area of the square: $A_{\text{sq}} = 4 \times 4 = 16 \text{ m}^2$
   3. Add the areas: $A_{\text{total}} = 40 + 16 = 56 \text{ m}^2$
   4. Trace the outside edges. The overall shape is a rectangle $14$ m long and $4$ m wide (the shared edge is internal, not on the boundary): $P = 2 \times (14 + 4) = 2 \times 18 = 36 \text{ m}$

   Answer: Total area $= 56$ m²; total perimeter $= 36$ m.

7. Volume of triangular prisms

   A triangular prism has a triangular cross-section with a base of $6$ cm and a perpendicular height of $5$ cm. The prism has a length of $10$ cm. Find the volume of the prism.

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   Key idea: The volume of a prism is the area of its cross-section multiplied by its length. For a triangular cross-section, use $A = \frac{1}{2} \times b \times h$.

   1. Find the area of the triangular cross-section: $A = \frac{1}{2} \times 6 \times 5 = 15$ cm²
   2. Write the volume formula: $V = A \times l$
   3. Substitute the values: $V = 15 \times 10$
   4. Calculate: $V = 150$

   Answer: The volume is $150$ cm³.

8. Capacity

   Mia is building a rectangular garden bed that is $2$ m long, $80$ cm wide and $25$ cm deep. She needs to fill it with soil. One bag of soil contains $40$ litres. How many whole bags of soil does Mia need to buy to completely fill the garden bed? (Note: $1$ litre $= 1000$ cm³)

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   Key idea: Convert all measurements to the same unit first, then find the volume and convert to litres to compare with the bag size.

   1. Convert all measurements to centimetres: length $= 200$ cm, width $= 80$ cm, height $= 25$ cm.
   2. Find the volume: $V = 200 \times 80 \times 25 = 400\,000$ cm³
   3. Convert to litres: $400\,000 \div 1000 = 400$ litres
   4. Find the number of bags: $400 \div 40 = 10$ bags

   Answer: Mia needs to buy $10$ bags of soil.

Free worksheets for this chapter

Worked examples and a free PDF with answers for each topic.

• Year 7 algebra worksheet
• Year 7 circles worksheet
• Year 7 area and perimeter worksheet
• Year 7 squares and square roots worksheet
• Year 7 volume worksheet