Grade 6 · Grade 6: Area, Volume and Surface Area · Measurement of Shapes and Solids
Area, Volume and Surface Area
Decompose polygons to find area, build nets for surface area and measure volume with fractional edge lengths.
Learning objectives
- Find areas of triangles, quadrilaterals and polygons by decomposition.
- Use nets to calculate surface area.
- Find volumes of prisms with fractional edge lengths.
- Draw polygons in the coordinate plane and find side lengths.
AERO Mathematics alignment
AERO.M6.GM.1
Find the area of triangles, special quadrilaterals and polygons by composing and decomposing shapes.
AERO.M6.GM.2
Find the volume of right rectangular prisms with fractional edge lengths using V = lwh and V = Bh.
AERO.M6.GM.3
Draw polygons in the coordinate plane given vertices, and use coordinates to find side lengths.
AERO.M6.GM.4
Represent three-dimensional figures using nets and use the nets to find surface area.
MYP criteria
- Criterion A — Knowing and understanding
- Criterion C — Communicating
- Criterion D — Applying mathematics in real-life contexts
ENGAGE
Start here
A tiler needs to cover an L-shaped floor and paint the walls of a rectangular storage box.
Think about it
How can one shape be measured by breaking it into simpler pieces?
Hint: Every polygon can be cut into rectangles and triangles.
EXPLAIN
Area, surface area and volume
Area by decomposition
A triangle is half of a rectangle with the same base and height, so A = ½bh. An L-shape can be split into two rectangles, or completed into one large rectangle with a piece removed.
| Shape | Formula | Note |
|---|---|---|
| Rectangle | A = lw | Base times height |
| Triangle | A = ½bh | Height is perpendicular to the base |
| Parallelogram | A = bh | Shear a rectangle |
| Trapezium | A = ½(a + b)h | Average of the parallel sides |
Nets and surface area
A net is the solid unfolded flat. Surface area is simply the total area of every face, so a rectangular prism has surface area 2(lw + lh + wh).
Volume with fractional edges
Volume counts unit cubes: V = lwh, or V = Bh where B is the base area. With fractional edges, such as 1½ × ¾ × 2, multiply the fractions directly rather than rounding first.
Remember
Area uses square units (cm²) and volume uses cubic units (cm³). If your units do not match the dimension, something has gone wrong.
INVESTIGATION
Try it yourself
Measure a real box at home. Sketch its net, calculate the surface area of card needed to make it and the volume it holds, then check whether the printed capacity matches your calculation.
Watch
Circles, Circumference and Area
Math Antics · 10:00
Builds the measurement habits you need for area and surface-area work.
Before you watch: Why does area use square units but perimeter does not?
- What is the area of a triangle with base 12 and height 5?
- How does a net help you find surface area?
Interactive simulation · PhET
Area Builder
Build shapes with a fixed area but different perimeters, then decompose them into triangles and rectangles.
While you explore
- Can two shapes have the same area but different perimeter? Show one example.
- How did decomposing the shape make the area easier to calculate?
Key vocabulary
- Surface area
- The total area of all the outside faces.
- Net
- A flat pattern that folds into a solid.
Practice questions
0/1 correct
Level 1 · Criterion A
A triangle has base 10 cm and height 6 cm. What is its area?
MYP criterion tasks
Level 2 · Criterion C
A box measures 1½ m by ¾ m by 2 m. Find its volume and explain your method.
Reflect & track
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