NCERT Class 10 Maths Lab Manual – Areas of Sectors formed at the Vertices of a Triangle
To verify that sum of areas of three sectors of the same radii ‘r’ formed at the vertices of any triangle is πr2 by paper cutting and pasting.
- Concept of different types of triangles.
- Definition of a sector.
- Area of circle = πr2, r → radius.
Glazed paper, sketch pens, fevicol, a pair of scissors, pencil, geometry box.
- 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).
The shape formed on the straight line is a semi circle
∴ area of circle = πr2
∴ area of semicircle = πr2
It is verified that the sum of areas of three sectors of same radii ‘r’ formed at the vertices of any triangle is πr2.
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.
- Find the sum of areas of four sectors of same radii ‘r’ formed at the vertices (as centre) of any quadrilateral through activity.
- Find the sum of areas of five sectors of same radii ‘r’ formed at the vertices (as centre) of any pentagon through activity.
What is the angle subtended by a circle at centre ?
What is the sum of angles of four sectors of same radii ‘r’ formed at the vertices (as centre) at any quadrilateral ?
If the perimeter of semicircle is 12 cm, find its radius.
What is the area of a semicircle of radius 2 cm ?
Define a segment of a circle.
A chord divides a circle in two parts each of which is called a segment of a circle.
What is the difference between a sector and a segment of a circle ?
A sector of a circle is formed by an arc and two radii of the circle, while a segment is one of its part in which a chord divides a circle.
A line segment joining two points on the circumference of a circle is known as a chord.
“A tangent intersects the circle in more than one point”. Is the statement true or false ?
Multiple Choice Questions
If the area of a semicircle is 121 cm2, find its radius.
(a) √77 cm
(b) √76 cm
(c) √74 cm
(d) None of these
If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(a) π units
(b) 2 units
(c) 4 units
(d) 5 units
Area of a sector of angle P (in degree) of a circle witl radius R is
Area of the sector of a circle with radius 4 cm and angle 30° is
(a) 4.91 cm
(b) 14.9 cm
(c) 4.19 cm
Find the area of a quadrant of circle whose circumference is 22 cm.
Find the perimeter of the quadrant of a circle of radius 4.2 cm.
(d) 15 cm
(b) 8.4 cm
(c) 12.6 cm
(d) None of these
If the radius of a circle is increased by 100% by what percent is the area of the circle increased ?
(d) None of these
The perimeter of a sector with radius r and angle θ of a circle is given by
Area of the sector of a circle with radius 7 cm and angle 120° is
(a) 51.33 cm2
(b) 53.11 cm2
(c) 53.13 cm2
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.