Class 4 — Mathematics

Measurement and Geometry: Perimeter, Angles, and Circles

Class 4

✓By the end of this lesson students will be able to define and calculate the perimeter of simple closed figures like squares and rectangles.
✓By the end of this lesson students will be able to identify and classify different types of angles (right, acute, obtuse) visually.
✓By the end of this lesson students will be able to identify and label the parts of a circle (centre, radius, diameter).
✓By the end of this lesson students will be able to draw a circle using a compass with a given radius.

Key concepts

Perimeter

The perimeter of a closed figure is the total length of its boundary. To find the perimeter, we add the lengths of all its sides. For example, if you walk along the boundary of a park, the total distance you walk is its perimeter.

Perimeter of a square = 4 × side; Perimeter of a rectangle = 2 × (length + breadth)

Angles

An angle is formed when two rays meet at a common point called the vertex. We can see angles all around us, like the corner of a room, the hands of a clock, or the edges of a book. There are different types of angles:\n1. Right Angle: An angle that looks like the corner of a square or a capital 'L'.\n2. Acute Angle: An angle that is smaller than a right angle.\n3. Obtuse Angle: An angle that is larger than a right angle but smaller than a straight line.

Circles

A circle is a closed curved shape where all points on the curve are at the same distance from a fixed point inside it. This fixed point is called the centre of the circle. Let's learn about the parts of a circle:\n1. Centre: The fixed point from which all points on the circle are equally distant.\n2. Radius: The distance from the centre to any point on the circle. All radii of a circle are equal.\n3. Diameter: A line segment that passes through the centre of the circle and connects two points on the circle. The diameter is the longest line segment that can be drawn inside a circle. The diameter is always twice the length of the radius.

Diameter = 2 × Radius

Key facts to remember

1Perimeter is the total length of the boundary of a closed figure.
2To find the perimeter, add the lengths of all sides of the figure.
3A right angle looks like the corner of a square.
4An acute angle is smaller than a right angle.
5An obtuse angle is larger than a right angle.
6The centre is the fixed point inside a circle.
7The radius is the distance from the centre to any point on the circle.
8The diameter is a line segment passing through the centre and connecting two points on the circle.
9Diameter is always twice the radius (Diameter = 2 × Radius).

Worked examples

Example 1

Find the perimeter of a rectangular garden with length 15 metres and breadth 10 metres.

IGiven: Length (l) = 15 m, Breadth (b) = 10 m

IIFormula for perimeter of a rectangle = 2 × (l + b)

IIIPerimeter = 2 × (15 m + 10 m)

IVPerimeter = 2 × (25 m)

VPerimeter = 50 m

Answer

The perimeter of the rectangular garden is 50 metres.

Remember to include the correct unit in your final answer.

Example 2

Look at the following angles and identify them as acute, right, or obtuse angle:

IAngle A: This angle is smaller than a right angle. So, it is an acute angle.

IIAngle B: This angle forms a perfect square corner. So, it is a right angle.

IIIAngle C: This angle is larger than a right angle. So, it is an obtuse angle.

Answer

Angle A: Acute Angle, Angle B: Right Angle, Angle C: Obtuse Angle

You can use the corner of your book or a set square to check if an angle is a right angle.

Example 3

Draw a circle with a radius of 4 cm. Label its centre, radius, and diameter.

I1. Take a compass and a ruler.

II2. Place the pointer of the compass at the 0 mark on the ruler and open the pencil arm to 4 cm.

III3. Place the pointer on a sheet of paper and rotate the pencil arm completely to draw the circle.

IV4. Mark the point where the compass pointer was placed as 'O' (Centre).

V5. Draw a line segment from the centre 'O' to any point on the circle, say 'A'. This is the radius (OA = 4 cm).

VI6. Draw a line segment passing through the centre 'O' and connecting two points on the circle, say 'B' and 'C'. This is the diameter (BC = 8 cm).

Answer

A correctly drawn circle with centre 'O', radius 'OA' (4 cm), and diameter 'BC' (8 cm) passing through 'O'.

Ensure the diameter passes exactly through the centre of the circle.

Common mistakes

✗Confusing perimeter with area (perimeter is length of boundary, area is space inside).
✗Forgetting to add all sides when calculating perimeter of irregular shapes.
✗Misidentifying acute and obtuse angles, especially when they are close to a right angle.
✗Drawing a circle freehand instead of using a compass, resulting in an oval shape.
✗Drawing the diameter without ensuring it passes through the centre of the circle.

Exam tips

★Always read the question carefully to understand what is being asked (perimeter, angle type, or circle part).
★Use a ruler to measure lengths accurately for perimeter problems.
★Use a compass for drawing circles to ensure they are perfectly round.
★Practice identifying angles in real-life objects to improve your visual recognition.

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