Area of Triangles & Parallelograms
Match Shape to Formula
Draw a line to match each shape to its area formula.
Triangle Area — Foundational
Use A = ½ × base × height. Circle the correct area.
Base = 6 cm, Height = 4 cm
Base = 10 m, Height = 7 m
Base = 8 cm, Height = 5 cm
Parallelogram Area — Foundational
Use A = base × height. Circle the correct area.
Base = 7 cm, Height = 5 cm
Base = 9 m, Height = 4 m
Base = 11 cm, Height = 6 cm
Draw and Label Shapes
Draw the shape described and label the dimensions used to find area.
Draw a triangle with base 5 cm and height 4 cm. Which two dimensions do you need to calculate its area?
Draw a parallelogram with base 8 cm and height 3 cm. Label the base and the perpendicular height (not the slant side).
Sort from Smallest to Largest Area
Calculate the area of each shape, then sort from smallest to largest.
Real-World Triangle Areas
Solve each area problem and show your working.
A triangular piece of coloured paper has base 15 cm and height 8 cm. What is its area?
A triangular garden bed has base 6 m and height 4 m. How much mulch (in m²) is needed to cover it?
Area Patterns — Triangle Heights
A triangle has a fixed base of 6 cm. Its height increases by 2 cm each step. Fill in the sequence of areas.
Unit Recognition
Circle the correct unit for each measurement.
The area of a room measured in metres
The perimeter of a rectangle measured in centimetres
The volume of a box measured in metres
The area of a triangle measured in millimetres
Perimeter vs Area
Answer these questions about the difference between perimeter and area.
A rectangle has length 8 cm and width 5 cm. Find both its perimeter and its area. Which is larger?
Two shapes have the same perimeter of 24 cm. Can they have different areas? Give an example.
Match Unit to Measurement Type
Sort each measurement into the correct column.
Composite Shape — Rectangle and Triangle
Find the total area by splitting the composite shape into simpler parts.
A shape is made of a rectangle (8 cm × 5 cm) with a triangle on top (base 8 cm, height 3 cm). Find the total area.
A shape is made of a parallelogram (base 10 m, height 4 m) with a triangle removed from one corner (base 4 m, height 4 m). Find the remaining area.
L-Shape Areas
Split each L-shape into two rectangles and find the total area.
L-shape: large rectangle 10×6 cm, small cut-out 4×2 cm. Total area?
L-shape: two rectangles joined — 5×8 m and 3×4 m. Total area?
L-shape: 9×7 cm minus a 3×3 cm corner. Total area?
Missing Dimension — Developing
Rearrange the area formula to find the unknown. Show all steps.
A triangle has area 45 cm² and height 9 cm. What is the base?
A parallelogram has area 84 m² and base 12 m. What is the perpendicular height?
A triangular sail has area 15 m² and base 5 m. What is its height?
Match Formula to Shape Description
Draw a line to match each description to the correct area formula.
Tiling and Area
Answer these tiling problems using area calculations.
A floor tile is a square with side 30 cm. How many tiles are needed to cover a rectangle 3 m × 2.4 m? Show your working.
Triangular tiles (base 20 cm, height 15 cm) are used to decorate a wall panel 1 m × 1 m. How many tiles fit exactly in the panel?
Unit Conversion Problems
Circle the correct conversion.
Convert 2 m² to cm²
Convert 150 000 cm² to m²
A floor tile covers 900 cm². How many tiles are needed to cover 2 m²?
Garden Design Problem
Plan a garden using area calculations.
A garden is rectangular, 12 m × 8 m. Inside the garden there is a triangular pond (base 4 m, height 3 m) and a parallelogram-shaped lawn (base 6 m, height 5 m). What area remains for planting?
Area Pattern — Parallelograms
A parallelogram has a fixed height of 5 cm. Its base increases by 3 cm each step. Fill in the missing areas.
Comparing Areas of Different Shapes
Investigate how different shapes with the same perimeter can have different areas.
A triangle and a parallelogram both have a base of 8 cm. The triangle has height 6 cm; the parallelogram has height 4 cm. Which has the larger area and by how much?
A square has the same perimeter as a rectangle 12 cm × 2 cm. Find both areas. Which shape covers more surface?
Real-World: Painting a Wall
Solve this real-world area problem.
A wall is rectangular, 4 m wide and 3 m tall. It has a triangular window cut into it (base 1.5 m, height 1.2 m). Paint covers 10 m² per litre. How much paint is needed (to the nearest 0.1 L) to paint the wall?
Sort by Area — Largest to Smallest
Calculate each area, then sort from largest to smallest.
Area Scaling
Circle the correct answer.
A triangle has area 20 cm². Its base and height are both doubled. What is the new area?
A parallelogram has area 30 m². Its base is tripled but its height stays the same. New area?
A square has area 16 cm². Its side is halved. New area?
Justify Your Strategy
Explain how you would approach each problem.
A composite shape looks like the letter 'L'. Describe TWO different ways you could split it to find its area.
A student says the area of a parallelogram with base 8 cm and slant side 6 cm is 48 cm². Is the student correct? Explain.
Investigating Perimeter and Area Relationships
Explore the relationship between perimeter and area.
List 4 different rectangles that each have a perimeter of 20 cm. Calculate the area of each. What do you notice?
Which rectangle with perimeter 20 cm has the largest area? What shape does this suggest gives the maximum area for a fixed perimeter?
Composite Shapes — Complex
Find the shaded area for each composite shape. Show all steps.
A rectangle 14 cm × 10 cm contains two triangles, each with base 6 cm and height 5 cm. What is the area of the rectangle NOT covered by the triangles?
A parallelogram with base 20 m and height 12 m has a rectangular hole 4 m × 3 m cut out. What is the remaining area?
Area Sequences — Mixed Shapes
Fill in the missing area in each sequence.
Cross-Sections and Area
Identify and calculate areas of cross-sections.
A prism has a triangular cross-section with base 8 cm and height 5 cm. What is the area of the cross-section? Why is cross-sectional area important for calculating volume?
A swimming pool has a trapezoidal cross-section. The two parallel sides are 1.2 m (shallow end) and 2.8 m (deep end), and the pool is 25 m long. If you know the cross-sectional area, explain how you would find the volume.
Problem-Solving: Fencing and Area
Solve this two-part problem about fencing and area.
A triangular paddock has sides of 40 m, 60 m, and 50 m. The perpendicular height to the base of 60 m is 33.3 m. Find the area of the paddock. If fencing costs $25 per metre, how much does it cost to fence the entire paddock?
Area Proof — Parallelogram from Rectangle
Explain the geometric proof that connects the area of a parallelogram to a rectangle.
Draw a parallelogram with base 8 cm and height 5 cm. Describe how cutting and rearranging it shows its area equals a rectangle with the same base and height.
Using the same idea, explain why the area of a triangle is HALF the area of a parallelogram with the same base and height.
Design a Shape with a Given Area
Use your knowledge of area formulas to design shapes to specification.
Design a triangular logo with area exactly 60 cm². Give two different pairs of base and height values that would work.
Design an L-shaped garden with total area between 40 m² and 50 m². Label all dimensions.
Connecting Area to Rate Problems
Solve these problems that connect area with a rate.
A triangular field has base 120 m and height 80 m. Grass seed costs $2.50 per m². What is the total cost of seeding the field?
Solar panels produce 150 W per m². A parallelogram-shaped panel array has base 6 m and height 4 m. How many watts does the array produce?
Area — Harder Calculations
Circle the correct area.
Triangle: b = 13 cm, h = 8 cm
Parallelogram: b = 14.5 m, h = 6 m
Composite: rectangle (12×5 m) + triangle (b=12, h=4 m)
Geometry in the News
Find a real-world reference and apply area calculations.
Research the area of a standard AFL oval (approximately 185 m × 155 m on average). If it were a parallelogram, what base and height might give that area? Compare with the actual oval shape.
Rank by Area Efficiency
Sort these shapes from most area per unit of perimeter to least.
Trapezium Area
Extend your knowledge to trapeziums.
A trapezium has parallel sides of 6 cm and 10 cm and a perpendicular height of 4 cm. Use A = ½(a + b)h to find its area.
Show that a parallelogram is a special case of a trapezium. What happens when both parallel sides are equal in the formula?
Coordinate Geometry — Area on a Grid
Use coordinates to calculate area.
A triangle has vertices at (0,0), (8,0), and (4,6). What is its area? (Hint: base = 8, height = 6.)
A parallelogram has vertices at (0,0), (5,0), (7,4), and (2,4). What is its area? What are the base and the perpendicular height?
Surface Area Preview — Triangular Prism
Calculate the surface area of a triangular prism.
A triangular prism has two triangular faces (base 6 cm, height 4 cm) and three rectangular faces (lengths 10 cm, widths 5 cm, 5 cm, and 6 cm). Find the total surface area.
Proof by Rearrangement
Construct a geometric argument using area.
A right-angled triangle has legs a and b and hypotenuse c. Four copies of this triangle are arranged around a square of side c. Show that the total area of the large square equals a² + b² + 4 × (½ab). Simplify to derive a² + b² = c².
Surveying and Area
Apply area knowledge to a land surveying context.
A surveyor maps an irregularly shaped block of land as a composite of two triangles and a parallelogram. Triangle 1: base 30 m, height 20 m. Triangle 2: base 25 m, height 16 m. Parallelogram: base 40 m, height 18 m. What is the total area of the block? If land in this area sells for $850/m², what is the block's value?
Area of a Regular Hexagon
Calculate the area of a regular hexagon using triangles.
A regular hexagon has side length 6 cm. Each of the 6 equilateral triangles has base 6 cm and height approximately 5.2 cm. Calculate the total area of the hexagon.
How does the area of a regular hexagon with side s compare to a circle with the same 'radius' s? Which covers more area?
Design Challenge: Maximum Area Enclosure
Apply area optimisation to a real design problem.
You have 100 m of fencing to enclose a rectangular field. Complete a table with different length-width pairs (perimeter = 100 m). Find the dimensions that maximise the enclosed area and explain the pattern you observe.
What if the field is triangular? Investigate whether a right-angled triangle or equilateral triangle (with the same perimeter) encloses more area. Write a conclusion.
Area Measurement at Home
Find and calculate areas of real shapes around you.
- 1Find a triangular piece of card or fabric. Measure its base and height and calculate its area. Check by cutting and rearranging it into a rectangle.
- 2Sketch the floor plan of a room as an L-shape or composite shape. Measure all dimensions and calculate the total floor area.
- 3Look at a wall or floor tile: measure its dimensions and calculate how many tiles would cover 1 m². Then count the actual tiles in a 1 m × 1 m section and compare.
- 4Research the area of a local park or sports ground. Use Google Maps (measure tool) to estimate the area, then compare with the formula for the best-fitting shape.