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Measure - Perimeter of 2D shapes

Grade 3Cambridge (IGCSE)

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

🔑Concepts

•

The perimeter of a rectangle can be found by adding the length and the width, and then multiplying the sum by 22, because a rectangle has two pairs of equal sides.

•

For a square, since all four sides are the same length, the perimeter is simply 44 times the length of one side.

📐Formulae

Perimeter of any polygon=sum of all side lengths\text{Perimeter of any polygon} = \text{sum of all side lengths}

Perimeter of a Square=4×s\text{Perimeter of a Square} = 4 \times s

Perimeter of a Rectangle=2×(l+w)\text{Perimeter of a Rectangle} = 2 \times (l + w)

💡Examples

Problem 1:

Find the perimeter of a triangle with side lengths 5cm5 cm, 12cm12 cm, and 13cm13 cm.

Solution:

Perimeter=5+12+13=30cm\text{Perimeter} = 5 + 12 + 13 = 30 cm

Explanation:

To find the perimeter of a triangle, we add the lengths of all three sides together.

Problem 2:

A square garden has a side length of 8m8 m. What is the total length of the fence needed to go around it?

Solution:

Perimeter=4×8=32m\text{Perimeter} = 4 \times 8 = 32 m

Explanation:

A square has 4 equal sides. We multiply the length of one side (8m8 m) by 4 to get the total perimeter.

Problem 3:

Calculate the perimeter of a rectangle with a length of 10cm10 cm and a width of 4cm4 cm.

Solution:

Perimeter=2×(10+4)=2×14=28cm\text{Perimeter} = 2 \times (10 + 4) = 2 \times 14 = 28 cm

Explanation:

Using the formula 2×(l+w)2 \times (l + w), we first add the length and width (10+4=1410 + 4 = 14) and then multiply by 2.

Problem 4:

Find the perimeter of an irregular shape with sides: 3cm3 cm, 2cm2 cm, 4cm4 cm, 5cm5 cm, and 6cm6 cm.

Solution:

3245+620\begin{array}{r} 3 \\ 2 \\ 4 \\ 5 \\ + 6 \\ \hline 20 \end{array} Perimeter=20cm\text{Perimeter} = 20 cm

Explanation:

For any polygon, we simply add all the exterior side lengths together.