Writing Patterns in Geometry

Q. What is the general rule that gives the number of matchsticks in terms of the number of triangles as shown in the figure?

1. $4x+1$
2. $3x+1$
3. $2x+1$
4. $2x$

Q.

Question 4

The diameter of a circle is a line, which joins two points on the circle and also passes through the centre of the circle. (In the adjoining figure AB is a diameter of the circle; C is its centre). Express the diameter of the circle (d) in terms of its radius (r).

Q. Using the variable n, what is the rule which gives the number of matchsticks required to make the following matchstick pattern?

1. $3n$
2. $2n$
3. $n$
4. $4n$

Q.

Question 11(ii)

Fig. below gives a matchstick pattern of triangles. As in Exercise 11(a) above, find the general rule that gives the number of matchsticks in terms of the number of triangles.

Q.

Find the rule, which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.

A pattern of letter Z as

Q.

Question 11(i)

Look at the following matchstick pattern of squares. The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares. (Hint: If you remove the vertical stick at the end, you will get a pattern of Cs.)

Q. The side of a regular hexagon is denoted by $l$. What do we get on expressing the perimeter of the hexagon using $l$ ?

1. $4l$
2. $2l$
3. $3l$
4. $6l$

Q.

Find the pattern followed in figures given below and number of matchsticks to be used in the ${47}^{th}$ figure$.$

Q.

Question 1(iii)

Find the rule, which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule
A pattern of letter U as

Q. The number 6 cannot be shown as a

1. square
2. line
3. rectangle
4. triangle

Q.

Question 1(vii)

Find the rule, which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.
A pattern of letter A as

Q.

Question 1(iv)

Find the rule, which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule
A pattern of letter V as

Q. The side of an equilateral triangle is shown by $l$. What do we get when we express the perimeter of the equilateral triangle using $l$?

1. $4l$
2. $5l$
3. $3l$
4. $2l$

Q.

Use the given algebraic expression to complete the table of number patterns.

If the number of digits formed is taken to be $\mathrm{n}$, the number of segments needed to form n digits is given by the algebraic expression appearing on the right of each pattern.

How many segments are needed to form $5,10,100$ digits of the kind

Q.

If the side of equilateral triangle is $l$, then express the perimeter of the triangle in terms of $l$.

Q. Which of the following numbers when represented in the form of dots can be arranged in the form of a line, rectangle or a square?

1. 2
2. 3
3. 4
4. 5

Q.

Five times a number divided by another number

Q. Show two different ways in which 18 can be represented as a rectangle.

Q.

Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule. A pattern for letter

Q.

Question 1(v)

Find the rule, which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.
A pattern of letter E as

Q. Write the rule to form the following pattern with match sticks.

Q.

Observe the pattern given below

Then term at $n^{th}$ position will be given by expression

1. 

2. 

3. $n\ast (n-1)$

4. 

Q.

How many matchsticks are needed to make four 8s?

1. 40

2. 42

3. 44

4. 46

Q. Look at the following matchstick pattern of squares. The squares are not separate. Two neighbouring squares have a common matchstick. What is the rule that gives the number of matchsticks in terms of the number of squares?
(Let the number of squares be x)

1. $3x+1$
2. $5x+1$
3. $4x+1$
4. $2x+1$

Q.

The side of an equilateral traingle is shown by $l$. Express the perimeter of equilateral triangle using $l$

Q. Which of the following is the perimeter of a regular hexagon of side '$s$' units?

1. $12s$ units
2. $6s$ units
3. $6s^2$ sq units
4. $-6s$ units

Q. Find the rule, which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule. A pattern of letter T as:

Q. The perimeter of the triangle shown below is

1. $x$ + $y$
2. 2$x$ + $y$
3. $x$ + 2$y$
4. 2$x$ $-$ $y$

Q. The side of an equilateral triangle is shown by $l$. Express the perimeter of the equilateral triangle using $l$.

Q. Find the rule which gives the number of match sticks required to make the following match sticks patterns.
A pattern of letter 'T'