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Geometry - Properties of 2D shapes (polygons and circles)

Grade 3Cambridge (IGCSE)

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

🔑Concepts

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A polygon is a 2D closed shape with straight sides. A regular polygon has all sides equal and all angles equal, whereas an irregular polygon has sides or angles of different sizes.

Comparison between a regular square and an irregular quadrilateral.
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Polygons are named based on their number of sides: Triangle (3), Quadrilateral (4), Pentagon (5), Hexagon (6), Heptagon (7), and Octagon (8).

A pentagon shape showing 5 sides and 5 vertices.
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The parts of a circle include the center, the radius (distance from center to edge), the diameter (line across through the center), and the circumference (the boundary).

Diagram of a circle showing the radius, diameter, and center point.
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A quadrilateral is any four-sided polygon. Common types include the square, rectangle, rhombus, and trapezoid. Each has unique properties regarding parallel lines and side lengths.

📐Formulae

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

Number of vertices = Number of sides (for any polygon)\text{Number of sides (for any polygon)}

Diameter=2×Radius\text{Diameter} = 2 \times \text{Radius}

💡Examples

Problem 1:

A shape has 6 straight sides of equal length. What is the name of this shape, and is it regular or irregular?

Solution:

Regular Hexagon

Explanation:

A six-sided polygon is called a hexagon. Because all sides are mentioned as being equal in length, it is classified as 'regular'.

Problem 2:

If the radius of a circle is 5 cm5\text{ cm}, what is the length of its diameter?

Solution:

10 cm10\text{ cm}

Explanation:

The diameter of a circle is always twice the length of the radius. So, 5 cm×2=10 cm5\text{ cm} \times 2 = 10\text{ cm}.

Problem 3:

A rectangle has two sides that are 8 cm8\text{ cm} long and two sides that are 3 cm3\text{ cm} long. Calculate the perimeter.

Solution:

22 cm22\text{ cm}

Explanation:

The perimeter is the total distance around the shape. 8+8+3+3=22 cm8 + 8 + 3 + 3 = 22\text{ cm}.

Problem 4:

Calculate the perimeter of the irregular pentagon shown in the diagram, where the side lengths are 4 cm4\text{ cm}, 5 cm5\text{ cm}, 3 cm3\text{ cm}, 6 cm6\text{ cm}, and 4 cm4\text{ cm}.

An irregular pentagon with labeled side lengths.

Solution:

Perimeter=4+5+3+6+4=22 cm\text{Perimeter} = 4 + 5 + 3 + 6 + 4 = 22\text{ cm}

Explanation:

To find the perimeter of any polygon, we add the lengths of all its outer sides together.

Problem 5:

The diameter of a circular pond is 14 m14\text{ m}. What is the radius of the pond?

A circle representing a pond with a diameter line labeled 14m.

Solution:

Radius=Diameter2\text{Radius} = \frac{\text{Diameter}}{2} Radius=142=7 m\text{Radius} = \frac{14}{2} = 7\text{ m}

Explanation:

The radius is exactly half the length of the diameter, as it only goes from the center to the edge.