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Measurement - Area of compound shapes

Grade 6IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A compound (or composite) shape is a figure made up of two or more basic geometric shapes such as rectangles, squares, and triangles.

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The Decomposition Method involves splitting the compound shape into simpler, non-overlapping rectangles or triangles to calculate their areas individually.

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The Subtraction Method involves calculating the area of a larger 'bounding' rectangle and subtracting the area of the 'missing' pieces.

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Missing Side Lengths: Before calculating area, use the given dimensions to find any unknown lengths by looking at parallel sides.

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Units: Area is always measured in square units (e.g., cm2cm^2, m2m^2). Ensure all dimensions are in the same unit before starting calculations.

📐Formulae

Area of a Rectangle=extlength×extwidth\text{Area of a Rectangle} = ext{length} \times ext{width}

Area of a Square=extside2\text{Area of a Square} = ext{side}^2

Area of a Triangle=12×base×height\text{Area of a Triangle} = \frac{1}{2} \times \text{base} \times \text{height}

Total Area=Area of Shape A+Area of Shape B\text{Total Area} = \text{Area of Shape A} + \text{Area of Shape B}

💡Examples

Problem 1:

An L-shaped room has the following dimensions: a total height of 10m, a total width of 8m. The top horizontal edge is 4m and the right vertical edge is 6m. Find the total area.

Solution:

32 + 24 = 56 m2m^2

Explanation:

Split the 'L' into two rectangles. Rectangle 1 (top): 4m×(10m−6m)=4m×4m=16m24m \times (10m - 6m) = 4m \times 4m = 16m^2. Rectangle 2 (bottom): 8m×6m=48m28m \times 6m = 48m^2. Wait, re-evaluating split: Let's split vertically. Rect A is 4m4m wide by 10m10m high (40m240m^2). Rect B is (8m−4m)=4m(8m - 4m) = 4m wide and (10m−6m)=4m(10m - 6m) = 4m high? No, the right edge is 6m. Rect B is 4m4m wide by 6m6m high (24m224m^2). If we split vertically: Left part is 4×10=404 \times 10 = 40. Right part is (8−4)×6=4×6=24(8-4) \times 6 = 4 \times 6 = 24. Total = 40+24=64m240 + 24 = 64m^2.

Problem 2:

A shape consists of a rectangle with a base of 12cm and a height of 5cm, with a triangle sitting on top. The triangle has a height of 4cm and the same base as the rectangle. Calculate the total area.

Solution:

84 cm2cm^2

Explanation:

  1. Area of Rectangle = 12cm×5cm=60cm212cm \times 5cm = 60cm^2. 2. Area of Triangle = 12×12cm×4cm=24cm2\frac{1}{2} \times 12cm \times 4cm = 24cm^2. 3. Total Area = 60+24=84cm260 + 24 = 84cm^2.

Problem 3:

A square metal sheet with side 10cm has a smaller rectangular hole cut out of the center. The hole is 3cm by 2cm. What is the remaining area of the metal sheet?

Solution:

94 cm2cm^2

Explanation:

Use the subtraction method. 1. Area of the large square = 10cm×10cm=100cm210cm \times 10cm = 100cm^2. 2. Area of the rectangular hole = 3cm×2cm=6cm23cm \times 2cm = 6cm^2. 3. Remaining Area = 100cm2−6cm2=94cm2100cm^2 - 6cm^2 = 94cm^2.