Lab Manual: Areas of Sectors formed at the Vertices of a Triangle | Lab Manuals for Class 10 PDF Download

Objective

Prerequisite Knowledge

• Concept of different types of triangles.
• Definition of a sector.
• Area of circle = πr², r → radius.

Materials Required
Glazed paper, sketch pens, fevicol, a pair of scissors, pencil, geometry box.

Procedure

• Draw three different types of triangles on a glazed paper as shown in fig. (i).
  (i) Equilateral ∆ABC
  (ii) Isosceles ∆PQR
  (iii) Scalene ∆XYZ
  
• Cut an equilateral ∆ABC as shown in fig.(ii)
  
• Taking vertices A, B and C as centres of ∆ABC, draw three sectors of same radii r.
  
• Cut these three sectors and marked them as 1,2,3 and fill different colours.
  
• Draw a straight line and mark any point ‘O’ on it. Place three sectors 1,2, 3 adjacent to each other so that the vertices A, B, C coincide with ‘O’ without leaving any gap as shown in fig. (v).
  
• The same process (steps 1-5) can be taken up with isosceles triangle and scalene triangle fig. (i).

Observation
The shape formed on the straight line is a semi circle
∴ area of circle = πr²
∴ area of semicircle = 1/2 πr²

Result
It is verified that the sum of areas of three sectors of same radii ‘r’ formed at the vertices of any triangle is 1/2 πr².

Learning Outcome
The students are able to understand the concept of this activity through paper cutting. It is clear to them that a semicircle is always obtained, whatever be the type of a triangle.

Activity Time

• Find the sum of areas of four sectors of same radii ‘r’ formed at the vertices (as centre) of any quadrilateral through activity.
  Hint:
  
• Find the sum of areas of five sectors of same radii ‘r’ formed at the vertices (as centre) of any pentagon through activity.