Exercise 6.3 - Chapter 6 Information Processing Term 1 6th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Question $1 .$
How many Triangles are there in each of the following figures?

Solution:
(i) The single portions A, B, C, D, E, F, G and H are 8 triangles.

Taking the combination of $2 \mathrm{E} \& \mathrm{~F}, \mathrm{~F} \& \mathrm{G} \& \mathrm{H}$ and $\mathrm{E}$ \& 11 are 4 triangles. There are $8+4=12$ triangles.
(ii) The smaller portions A, B, C, D, E, F, G and H are 8 triangles. Combining 2 at a time $\mathrm{B} \& \mathrm{C}, \mathrm{D}$ \& $\mathrm{F}, \mathrm{F}$ \& $\mathrm{G}, \mathrm{A}$ \& $\mathrm{H}$ are 4 triangles. Taking 4 at a time
Combination of $\mathrm{B}, \mathrm{C}, \mathrm{D}$ and $\mathrm{E} ; \mathrm{D}, \mathrm{E}, \mathrm{F}$ and $\mathrm{G} ; \mathrm{F}, \mathrm{G}, \mathrm{H}$ and $\mathrm{A} ; \mathrm{H}, \mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are 4 triangles. Total triangles $=8+4+4=16$.

(iii) Every part $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}, \mathrm{F}, \mathrm{G}, \mathrm{H}, \mathrm{I}, \mathrm{J}, \mathrm{K}, \mathrm{L}, \mathrm{M}, \mathrm{N}, \mathrm{O}$ and $\mathrm{P}$ are 16 triangles.
Combining two at a time. $\mathrm{A}$ \& $\mathrm{B}, \mathrm{B}$ \& $\mathrm{C}, \mathrm{C}$ \& $\mathrm{D}, \mathrm{D}$ \& $\mathrm{A}, \mathrm{J}$ \& $\mathrm{K}, \mathrm{L}$ \& $\mathrm{M}, \mathrm{N}$ \& $\mathrm{O}, \mathrm{P}$ \& $\mathrm{I}$ are 8 triangles. Taking the combination of 4, we have $\mathrm{I}, \mathrm{J}, \mathrm{E} \& \mathrm{~A} ; \mathrm{K}, \mathrm{L}, \mathrm{F}$ and $\mathrm{B}, \mathrm{M}, \mathrm{N}, \mathrm{G}$ and $\mathrm{C}, \mathrm{P}, \mathrm{O}, \mathrm{H}$ and $\mathrm{D}$ are 4 triangles.
Taking 8 parts together we have QRS, RST, STQ, and TRQ are 4 triangles.
Total triangles $=16+8+4+4=32$ triangles.

(iv)Taking smaller triangles we have AFB, BFG, BGC, CGH, HCD, DHI, DIE, EIJ, EJAand AJF $\Rightarrow 10$ triangles.
Taking the combination of 2 .
$\mathrm{CGD}, \mathrm{CID}, \mathrm{DJE}, \mathrm{DHE}, \mathrm{EIA}, \mathrm{EFA}, \mathrm{AGB}, \mathrm{AJB}, \mathrm{BHC}$ and $\mathrm{BFC}$ are 10 triangles.
Combining 3 at a time we have CED, DAE, EBA, ACB, BDC, CEF, DBJ, GDA, EBH, ACI $\Rightarrow 10$ triangles.
Other triangles are BCE, CAD, DBE, ADB and ACE are 5 triangles.
Total $10+10+10+5=35$ triangles.

Question 2 .
Find the number of dots in the tenth figure of the following pattern.

Solution: (i) The number of dots given are $1,3,6,10,15, \ldots$

1st number $=1$
2 nd number $=1+2=3$
$3 \mathrm{rd}$ number $=3+3=6$
4 th number $=6+4=10$
5 th number $=10+5=15$
6 th number will be $15+6=21$
7 th number will be $21+7=28$
8 th number will be $28+8=36$
9 th number will be $36+9=45$
10 th number will be $45+10=55$
1st number $=1$
2nd number $=1+2=3$
3rd number $=3+3=6$
4th number $=6+4=10$
5th number $=10+5=15$
6th number will be $15+6=21$
7 th number will be $21+7=28$
8 th number will be $28+8=36$
9 th number will be $36+9=45$
10 th number will be $45+10=55$
Number of dots in the 10 th figure $=55$
(ii) The number of dots given are $1,4,9,11,16,25, \ldots$
The no. of dots are in the pattern $1 \times 1,2 \times 2,3 \times 3,4 \times 4,5 \times 5, \ldots \ldots 10 \times 10$
The number of dots in the 10 th figure $=100$.
Number of dots in the 10 th figure $=55$
(ii) The number of dots given are $1,4,9,11,16,25, \ldots$
The no. of dots are in the pattern $1 \times 1,2 \times 2,3 \times 3,4 \times 4,5 \times 5, \ldots \ldots 10 \times 10$
The number of dots in the 10 th figure $=100$.

Question 3.

(i) Draw the next pattern.
(ii) Prepare a table for the number of dots used for each pattern.
(iii) Explain the pattern.
(iv) Find the number of dots in the 25 th pattern.
Solution:

First number is 2
2 nd number is $2+3=5$
3 rd number is $5+4=9$
4 th number is $9+5=14$
5 th number is $14+6=20$
(iv) Number of dots in the 25 th pattern is

The number of dots in the 25 th pattern $=350$.

Question $4 .$
Count the number of squares in each of the following figures?

Solution:

Smaller squares $4 \times 4=16$ (As numbered).
As a whole bigger $=4$
Total squares $=20$

As we see in the figure in the middle $1,2,3$, and 4 are 4 small squares.
Also, we have 9 and $10=2$ big squares.
Outer squares $5,6,7, \& 8=4$.
Total $=4+4+1+1=10$ squares.

Question 5 .
How many circles are there in the following figure?

Solution:

There are 7 Circles.

Question 6.

Find the minimum number of straight lines used in forming the following figures

Solution:

There are 5 horizontal lines and 5 vertical lines. Total of 10 lines minimum needed.

There are 12 straight lines used which is minimum.