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Measurement - Calculating the perimeter and area of composite shapes

Grade 4Cambridge (IGCSE)

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

🔑Concepts

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

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Perimeter is the total distance around the outside of the shape. To find it, you must ensure all side lengths are known and then add them together.

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To find the area of a composite shape, 'decompose' (split) it into smaller rectangles or squares, calculate the area of each, and add them together.

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Missing side lengths can be found by looking at parallel sides. For example, in an L-shaped figure, the total horizontal width is equal to the sum of the shorter horizontal segments.

📐Formulae

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

Area of a Square=side×side\text{Area of a Square} = \text{side} \times \text{side}

Perimeter=Sum of all outer sides\text{Perimeter} = \text{Sum of all outer sides}

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 figure has a total height of 8 cm and a total width of 10 cm. The top horizontal side is 4 cm and the right-most vertical side is 3 cm. Calculate the Perimeter.

Solution:

36 cm

Explanation:

First, find the missing side lengths. The missing horizontal side is 10−4=610 - 4 = 6 cm. The missing vertical side is 8−3=58 - 3 = 5 cm. The perimeter is the sum of all sides: 10+8+4+3+6+5=3610 + 8 + 4 + 3 + 6 + 5 = 36 cm.

Problem 2:

A composite shape is made of two rectangles joined together. Rectangle A is 5 m by 4 m. Rectangle B is 3 m by 2 m. What is the total area?

Solution:

26 m²

Explanation:

Calculate the area of each rectangle separately. Area A=5×4=20 m2\text{Area A} = 5 \times 4 = 20 \text{ m}^2. Area B=3×2=6 m2\text{Area B} = 3 \times 2 = 6 \text{ m}^2. Add them together: 20+6=26 m220 + 6 = 26 \text{ m}^2.

Problem 3:

Find the area of a large 10 cm x 10 cm square that has a 3 cm x 2 cm rectangular piece cut out from one corner.

Solution:

94 cm²

Explanation:

Instead of adding, we subtract the smaller area from the larger one. Area of large square=10×10=100 cm2\text{Area of large square} = 10 \times 10 = 100 \text{ cm}^2. Area of the cut-out=3×2=6 cm2\text{Area of the cut-out} = 3 \times 2 = 6 \text{ cm}^2. Total Area = 100−6=94 cm2100 - 6 = 94 \text{ cm}^2.