krit.club logo

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

Grade 4IGCSE

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

🔑Concepts

•

Definition of Polygons: Closed 2D shapes made of three or more straight lines.

•

Regular vs. Irregular Polygons: Regular polygons have all sides and angles equal; irregular polygons do not.

•

Types of Triangles: Scalene (no equal sides), Isosceles (two equal sides), and Equilateral (three equal sides).

•

Quadrilaterals: Four-sided polygons including Squares, Rectangles, Parallelograms, Rhombuses, and Trapeziums.

•

Parts of a Circle: The Center (middle point), Radius (center to edge), Diameter (edge to edge through center), and Circumference (the perimeter).

•

Line Symmetry: A line that divides a shape into two identical mirror halves.

•

Rotational Symmetry: How many times a shape looks the same as it is rotated a full 360 degrees.

📐Formulae

Perimeter of a Polygon=Sum of all side lengths\text{Perimeter of a Polygon} = \text{Sum of all side lengths}

Area of a Rectangle=Length×Width\text{Area of a Rectangle} = \text{Length} \times \text{Width}

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

Sum of interior angles in any triangle=180∘\text{Sum of interior angles in any triangle} = 180^{\circ}

💡Examples

Problem 1:

A regular hexagon has one side length of 7 cm. What is its perimeter?

Solution:

42 cm

Explanation:

A hexagon has 6 sides. Since it is a 'regular' hexagon, all 6 sides are equal. Perimeter = 6×7 cm=42 cm6 \times 7\text{ cm} = 42\text{ cm}.

Problem 2:

If the radius of a circle is 5.5 cm, calculate the diameter.

Solution:

11 cm

Explanation:

The diameter is always twice the length of the radius. Diameter = 2×5.5 cm=11 cm2 \times 5.5\text{ cm} = 11\text{ cm}.

Problem 3:

In a right-angled triangle, one angle is 90∘90^{\circ} and another is 45∘45^{\circ}. Find the size of the third angle.

Solution:

45^{\circ}

Explanation:

The sum of angles in a triangle is 180∘180^{\circ}. So, 180∘−(90∘+45∘)=180∘−135∘=45∘180^{\circ} - (90^{\circ} + 45^{\circ}) = 180^{\circ} - 135^{\circ} = 45^{\circ}.

Problem 4:

Identify the quadrilateral that has two pairs of parallel sides, but no right angles and all four sides are equal.

Solution:

Rhombus

Explanation:

A square has four equal sides and right angles. A rhombus has four equal sides but its interior angles are not 90∘90^{\circ}.