E2.2 · Convert metric units in perimeter, area, and volume problems

Ontario Grade 7 Mathematics

Spatial Sense

Choose units that match what is measured, then convert carefully

What you will learn

• Name common metric units used for length, area, and volume.
• Convert between metric units using their place-value relationships.
• Solve perimeter, area, and volume problems while keeping units consistent.

1. Review metric units and measurement

• Length uses units such as mm, cm, and m.
• Perimeter measures around; area measures a surface; volume measures space inside.
• Write the unit with every measurement and answer.

2. Convert units before finding perimeter

• Convert side lengths to one unit before adding them.
• Perimeter is reported in a length unit, not a square unit.
• Check that the converted number represents the same distance.

3. Convert area units with square units

• Area is measured in square units, such as cm² or m².
• A length conversion factor is applied to each side of a square or rectangle.
• One square metre equals 10 000 square centimetres.

4. Convert volume units with cubic units

• Volume uses cubic units, such as cm³ or m³.
• For cubic units, the length conversion applies in three dimensions.
• One cubic metre equals 1 000 000 cubic centimetres.

Common metric conversions for this lesson

Worked example

Perimeter with mixed length units

1. Make the units match
   The width is already in centimetres. Convert the length from metres to centimetres so both measurements can be used together.
   $$1.8\text{ m}=180\text{ cm}$$
2. Add all four sides
   A rectangle has two sides of each given length. Add both lengths and both widths to find the distance around the sign.
   $$P=180+65+180+65=490\text{ cm}$$
3. Check the unit
   Perimeter is a distance, so centimetres are the correct kind of unit. The result is a reasonable length for the sign’s boundary.

Worked example

Area in square centimetres

1. Convert the length
   Convert 1.2 metres to centimetres. Then both dimensions will be in centimetres, which allows their product to give square centimetres.
   $$1.2\text{ m}=120\text{ cm}$$
2. Find the area
   Multiply the mat’s length by its width. Because each dimension is in centimetres, the area is in square centimetres.
   $$A=120\times80=9600\text{ cm}^2$$
3. Check the unit and size
   Area needs a square unit. The result is also less than the same area written in square metres, which is consistent because square centimetres are smaller units.
   $$9600\text{ cm}^2=0.96\text{ m}^2$$

Worked example

Volume and a large unit conversion

1. Use one length unit
   Convert 0.5 metres to centimetres so all three box dimensions use centimetres.
   $$0.5\text{ m}=50\text{ cm}$$
2. Find the volume
   Multiply length, width, and height. Since the three measurements are in centimetres, the product is in cubic centimetres.
   $$V=50\times40\times25=50\,000\text{ cm}^3$$
3. Compare with cubic metres
   There are 1 000 000 cubic centimetres in 1 cubic metre. Divide by 1 000 000 to express the same volume in cubic metres.
   $$50\,000\text{ cm}^3=0.05\text{ m}^3$$

Common mistakes and how to avoid them

Lesson summary

• Convert measurements to matching units before calculating.
• Perimeter is a sum of lengths and uses length units.
• Area uses square units; 1 m² equals 10 000 cm².
• Volume uses cubic units; 1 m³ equals 1 000 000 cm³.
• Check that the final unit matches what the problem asks you to measure.

Check your understanding

Key terms

Perimeter

The distance around the edge of a flat shape.

Area

The amount of flat surface inside a shape’s edges.

Volume

The amount of space inside a three-dimensional object.

Square unit

A unit for area, such as cm², based on squares with equal side lengths.

Cubic unit

A unit for volume, such as cm³, based on cubes with equal edge lengths.

Rectangular prism

A box-shaped solid with rectangular faces.

Continue through Grade 7 Math

View the complete Grade 7 Math Ontario Grade 7 Mathematics curriculum and lessons

• E2.1 · Relate volume in cubic centimetres to capacity in millilitres
• E2.3 · Connect radius, diameter, and circumference
• E1.1 · Classify cylinders, pyramids, and prisms by properties and symmetry
• E1.2 · Draw scaled top, front, side, and perspective views
• E1.3 · Perform dilations and describe similar shapes
• E1.4 · Translate, reflect, and rotate shapes on a Cartesian plane

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 7 Mathematics, expectation E2.2. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

Official curriculum reference

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