Practice Maths

Topic Review — Area

Mixed Practice — L66 – L67

This review covers all lessons in the Area topic. Try each question before checking your answers.

Review Questions

  1. Area of Parallelograms Fluency

    Find the area of each parallelogram (A = base × perpendicular height).

    1. Base = 8 cm, perpendicular height = 6 cm
    2. Base = 14 m, perpendicular height = 5 m
    3. Base = 9.5 cm, perpendicular height = 4 cm
    4. Base = 20 mm, perpendicular height = 7 mm
    5. A parallelogram has area 72 cm² and base 9 cm. Find the perpendicular height.
    6. A parallelogram has area 130 m² and perpendicular height 10 m. Find the base.

  2. Area of Triangles Fluency

    Find the area of each triangle (A = ½ × base × height).

    1. Base = 10 cm, height = 8 cm
    2. Base = 6 m, height = 9 m
    3. Base = 13 mm, height = 4 mm
    4. Base = 7.5 cm, height = 6 cm
    5. A triangle has area 36 m² and base 12 m. Find the height.
    6. A right-angled triangle has legs 10 cm and 7 cm. Find the area.

  3. Missing Dimensions Fluency

    1. Parallelogram: A = 56 cm², h = 7 cm. Find the base.
    2. Triangle: A = 45 m², base = 15 m. Find the height.
    3. Parallelogram: A = 84 mm², base = 12 mm. Find the height.
    4. Triangle: A = 30 cm², h = 10 cm. Find the base.

  4. Composite Shapes Understanding

    1. A shape consists of a rectangle (15 cm × 8 cm) with a triangle on top (base 15 cm, height 5 cm). Find the total area.
    2. A composite shape is a parallelogram (base 12 m, height 6 m) with a triangle cut out (base 4 m, height 6 m). Find the remaining area.
    3. A pentagon-shaped garden can be divided into a rectangle (10 m × 4 m) and a triangle (base 10 m, height 3 m). Find the total area of the garden.
    4. Two triangular sails each have base 6 m and height 8 m. A rectangular panel has dimensions 6 m × 3 m. Find the total area of both sails and the panel combined.

  5. Real-World Problems Problem Solving

    1. A parallelogram-shaped driveway has base 8 m and perpendicular height 4 m. Concrete costs $45 per m². Find the cost to concrete the driveway.
    2. A triangular garden has base 12 m and height 7 m. Fertiliser costs $5 per m². Find the cost of fertilising the garden.
    3. A wall consists of a rectangle (5 m × 3 m) with a triangular window removed (base 1.5 m, height 1 m). Find the area of wall that needs painting.
    4. A logo is made of two identical triangles (base 4 cm, height 6 cm) and a parallelogram (base 4 cm, height 3 cm) between them. Find the total area of the logo.
    5. Astroturf costs $18 per m². A sports field has a parallelogram shape with base 40 m and perpendicular height 25 m. Find the total cost of the turf.

  6. Choose the correct formula: Fluency

    1. Write the formula for the area of a triangle.
    2. Write the formula for the area of a parallelogram.
    3. A shape has base b and height h. Show that the area of a triangle is half the area of a parallelogram with the same base and height.

  7. Units of area: Fluency

    1. Convert 3.5 m² to cm².
    2. Convert 85 000 cm² to m².
    3. A room measures 4 m by 6 m. What is its area in m²? How many cm² is that?

  8. A triangle has base (2x + 3) cm and height 8 cm. Its area is 52 cm². Understanding

    1. Write an equation for the area of the triangle.
    2. Solve for x.
    3. What are the base and height of the triangle?

  9. A trapezium can be split into a parallelogram and a triangle. The trapezium has parallel sides of 5 m and 9 m, and a perpendicular height of 4 m. Understanding

    1. Sketch and label the trapezium split into a parallelogram and triangle.
    2. Find the area of the parallelogram section.
    3. Find the area of the triangle section.
    4. Find the total area of the trapezium.

  10. A community park is shaped like a large triangle with base 40 m and height 30 m. Inside the park there is a sandpit in the shape of a parallelogram (base 5 m, height 3 m). Problem Solving

    1. Find the area of the whole park.
    2. Find the area of the sandpit.
    3. What is the area of the park that is NOT sandpit?
    4. Grass seed costs $2.50 per m². How much does it cost to grass the non-sandpit area?
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