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Ratio of Areas of Two Similar Triangles Experiment Class 10 Maths Practical NCERT

The experiment to determine Ratio of Areas of Two Similar Triangles are part of the Class 10 Maths Lab Manual provides practical activities and experiments to help students understand mathematical concepts effectively. It encourages interactive learning by linking theoretical knowledge to real-life applications, making mathematics enjoyable and meaningful.

Maths Lab Manual Class 10 CBSE Ratio of Areas of Two Similar Triangles Experiment

Determine Ratio of Areas of Two Similar Triangles Class 10 Practical

Objective
To verify “The ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides” by performing an activity.

Prerequisite Knowledge

  1. Concept of parallel lines.
  2. Division of a line in a given ratio.

You can also download Class 10 Maths to help you to revise complete syllabus and score more marks in your examinations.

Materials Required
Chart paper, construction box, coloured pens, a pair of scissors, fevicol.

Procedure

  1. Take a chart paper and cut a ∆ABC with AB = 6cm, BC = 6cm, CA = 6cm.
  2. Mark 5 points P1, P2, …. , P5 at a distance of 1cm each on side AB and Q1, Q2,…..,Q5 at a distance of 1cm each on side AC as shown in fig.(i).
    NCERT Class 10 Maths Lab Manual - Ratio of Areas of Two Similar Triangles 1
  3. Join P1Q1, P2Q2, …………, P5Q5 as shown in fig. (ii).
    NCERT Class 10 Maths Lab Manual - Ratio of Areas of Two Similar Triangles 2
  4. Draw lines parallel to AC from P1, P2, P5 and also draw lines parallel to AB from the points Q1, Q2, ……., Q5 as shown in fig. (iii).
    NCERT Class 10 Maths Lab Manual - Ratio of Areas of Two Similar Triangles 3
  5. Thus ∆ABC is divided into 36 smaller triangles and all are similar to each other and of equal area.
  6. Construct a ∆PQR with PQ = \(\frac { 1 }{ 2 }\) of AB, PR = \(\frac { 1 }{ 2 }\) of AC and QR = \(\frac { 1 }{ 2 }\) of BC i.e. 3cm each on another chart paper.
  7. Mark D1, D2 and E1, E2 on sides PQ and PR respectively.
  8. Repeat steps 3 and 4.
  9. Thus ∆PQR is divided into 9 smaller similar triangles equal in area.
    NCERT Class 10 Maths Lab Manual - Ratio of Areas of Two Similar Triangles 4

Observation

  1. area of ∆ABC = area of 36 smaller ∆’s
  2. area of ∆PQR = area of 9 smaller ∆’s
  3. \(\frac {PQ}{AB}=\frac {3}{6} =\frac {1}{2} =\frac {PR}{AC}\)
  4. \(\frac { Area\quad of\quad \Delta PQR }{ Area\quad of\quad \Delta ABC } =\frac { { PQ }^{ 2 } }{ { AB }^{ 2 } }\)
    = [9 smaller Δ’s/36 smaller Δ’s = \(\frac { 1 }{ 4 }\) = (1/2)2
    (because ΔABC ∼ ΔPQR)

Result
Thus it is verified that the ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides.

Learning Outcome
Concept of area theorem is clear to the students through this activity.

Activity Time
1. Take isosceles similar triangles and scalene similar triangles and try to verify this activity. Here isosceles triangles, ∆ABC ~ ∆PQR. Scalene triangle ∆DEF ~ ∆KLM
NCERT Class 10 Maths Lab Manual - Ratio of Areas of Two Similar Triangles 5

Viva Voce

Question 1.
What are the criteria for two triangles to be similar ?
Answer:
Two triangles are said to be similar, if

  • their corresponding angles are equal.
  • their corresponding sides are in proportion

Question 2.
∆ABC ~ ∆DEF and their areas are respectively 64 cm2 and 121 cm2. If EF = 15.4 cm, then findBC.
Answer:
11.2 cm

Question 3.
Is it true, if the areas of two similar triangles are equal, then they are congruent ?
Answer:
Yes

Question 4.
What is the ratio of the area of an equilateral triangle described on one side of a square to the area of an equilateral triangle described on one of its diagonal ?
Answer:
1:2

Question 5.
Are a square and a rhombus of side 3 cm similar ?
Answer:
No

Question 6.
Is a rhombus of side 3 cm congruent to another rhombus of side 4 cm ?
Answer:
No

Question 7.
Is the ratio of the areas of two similar triangles equal to the square of the ratio of their corresponding medians ?
Answer:
Yes

Multiple Choice Questions

Question 1.
ABC and BDE are two equilateral triangles, such that D is the mid-point of BC. The ratio of the areas of ΔABC and ΔBDE is
(a) 2:1
(b) 1:2
(c) 4:1
(d) 1:4

Question 2.
Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio
(a) 2:3
(b) 4:9
(c) 81:16
(d) 16:81

Question 3.
If in two similar triangles PQR and LMN, if QR =15 cm and MN = 10 cm, then the ratio of the areas of triangles is
(a) 3:2
(b) 9:4
(c) 5:4
(d) 7:4

Question 4.
Two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 25. Then the ratio of their corresponding heights is
(a) 16 : 25
(b) 256 : 625
(c) 4 : 5
(d) none of these

Question 5.
∆ABC ~ ∆DEF. If AC = 19 cm and DF = 8 cm, then the ratio of the areas of the two triangles is
(a) 361 : 64
(b) 19 : 8
(c) 19 : 4
(d) none of these

Question 6.
In the given figure, PB and QA are perpendicular to segment AB. If PO = 5 cm, QO = 7 cm and area (∆POB) = 150 cm2, then area of ∆QOA is
NCERT Class 10 Maths Lab Manual - Ratio of Areas of Two Similar Triangles 6
(a) 254 cm2
(b) 294 cm2
(c) 244 cm2
(d) 49 cm2

Question 7.
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2CD, find the ratio of the areas of triangles AOB and COD.
(a) 4:1
(b) 1:4
(c) 4:4
(d) 2:4

Question 8.
ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, then the ratio of area (∆ABC) to area (∆DBC) is
(a) \(\frac {AO}{DO}\)
(b) \(\frac {AO}{ DB}\)
(c) \(\frac {AC}{DO}\)
(d) None of these

Question 9.
Area (∆ABC) : Area (∆DEF) = 25 : 36. Then AB : DE is
(a) 625 : 1296
(b) 25 : 36
(c) 6 : 5
(d) 5 : 6

Question 10.
∆DEF ~ ∆ABC; If DE : AB = 2 : 3 and area ∆DEF is equal to 44 square units, then area (∆ABC) is
(a) 120 sq. units
(b) 99 sq. units
(c) 66 sq. units
(d) none of these

Answers

  1. (c)
  2. (d)
  3. (b)
  4. (c)
  5. (a)
  6. (b)
  7. (a)
  8. (a)
  9. (d)
  10. (b)

Math LabsScience LabsScience Practical SkillsMath Labs with Activity

NCERT Class 10 Maths Lab Manual 

  • Determine Linear Equations Class 10 Experiment
  • Determine Basic Proportionality Theorem for a Triangle Class 10 Experiment
  • Determine Pythagoras Theorem Class 10 Experiment
  • Determine Ratio of Areas of Two Similar Triangles Class 10 Experiment
  • Determine Centroid of a Triangle Class 10 Experiment
  • Determine Arithmetic Progression I Class 10 Experiment
  • Determine Arithmetic Progression II Class 10 Experiment
  • Determine Sum of Odd Natural Numbers Class 10 Experiment
  • Determine Making of a Clinometer Class 10 Experiment
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