﻿ Geometric Patterns Worksheet | Problems & Solutions

# Geometric Patterns Worksheet

Geometric Patterns Worksheet
• Page 1
1.
Which of the following patterns follow the same rule as ABA ABA ABA?

 a. Pattern 4 b. Pattern 2 c. Pattern 1 d. Pattern 3

#### Solution:

In the given pattern ABA ABA ABA, A is followed by B, followed by A and so on.

In Pattern 2, a triangle is followed by a square, followed by a triangle and so on.

So, Pattern 2 follows the same rule as ABA ABA ABA.

2.
Which block comes next in the pattern?

 a. Block 4 b. Block 2 c. Block 1 d. Block 3

#### Solution:

The pattern is, two squares are removed to get the succeeding block.

So, Block 4 comes next in the pattern.

3.
If the pattern continues, how many blocks will there be as the sixth term of the pattern?

 a. 13 b. 11 c. 9 d. 12

#### Solution:

The rule for the pattern is to add 2 blocks to each figure to obtain the next figure in the pattern.

Number of blocks in the sixth term = Number of blocks in the fifth term + 2

= 9 + 2 = 11
[Number of blocks in the fifth term = Number of blocks in the fourth term + 2 = 7 + 2 = 9.]

So, there will be 11 blocks in the sixth term of the pattern.

4.
If the pattern continues, what would be the next figure in the pattern?

 a. Figure 1 b. Figure 4 c. Figure 2 d. Figure 3

#### Solution:

If you observe, in the first figure there is a square inside a triangle. That means, the outer polygon has 3 sides and the inner polygon has 4 sides.

In the second figure, there are 4 sides for the outer polygon and 5 sides for the inner polygon.

In the third figure, there are 5 sides for the outer polygon and 6 sides for the inner polygon.

So, the rule for the pattern is to add one side for both inner and outer polygons to obtain the next figure in the pattern.

So, the next figure should contain 6 sides as the outer polygon and 7 sides for the inner polygon.

So, Figure 4 is the next figure in the pattern.

5.
Name the missing polygon in increasing order of number of sides.

 a. pentagon b. hexagon c. decagon d. heptagon

#### Solution:

In the series, first polygon is having 3 sides, second polygon is having 4 sides and the fourth polygon is having 6 sides.

Third polygon should have 5 sides.

The polygon with 5 sides is known as pentagon.

So, the missing polygon is pentagon.

6.
Name the missing polygon in the series.

Pentagon, _______, Heptagon, Octagon.
 a. quadrilateral b. hexagon c. triangle d. circle

#### Solution:

In the series, the first polygon is pentagon which has 5 sides.

The third polygon is heptagon having 7 sides and fourth polygon is octagon having 8 sides.

So, the second polygon should have 6 sides.

The polygon with 6 sides is known as hexagon.

Missing polygon in the series is hexagon.

7.
Which animal among the choices will come next?

 a. Horse b. Lion

#### Solution:

The pattern is, one lion followed by two horses, followed by one lion and so on.

So, the next animal of the pattern will be a lion.

8.
Find the number of airplanes to be filled in the blank space of the sequence.

 a. 4 b. 10 c. 6 d. 8

#### Solution:

The number of aiplanes in the first place of the sequence = 8.

The number of aiplanes in the third place of the sequence = 4.

The number of aiplanes in the fourth place of the sequence = 2.

The number of aiplanes in each place of the sequence is obtained by subtracting two from the number of aiplanes of the previous place.

The number of aiplanes in the second place of the sequence = the number of aiplanes in the first place of the sequence - 2.

= 8 - 2
[Substitute the value.]

= 6
[Subtract.]

So, the number of aiplanes in the missing place of the sequence is 6.

9.
Which figure comes next in the pattern?

 a. square b. pentagon c. rectangle d. triangle

#### Solution:

The pattern is, a rectangle followed by a triangle, followed by a rectangle and so on.

So, the next figure of the pattern will be a rectangle of the same kind.

10.
Fill in the blank with the correct figure in the pattern.

 a. square b. circle c. rectangle d. triangle

#### Solution:

The pattern is, a circle followed by a triangle, followed by a circle and so on.

So, a circle of the same kind as in the pattern best fills the blank.