## Embedded Figure, Figure Formation, Construction of Squares, Grouping of Identical Figures and Figure Matrix

Category : 8th Class

EMBEDDED FIGURES

In this section, usually two types of problems are asked. Let us explain them briefly.

•          A simple figure (X) is provided. This figure (X) is embedded in any one of the four option figures.
•          A figure (X) is provided. This figure (X) embeds any one of the four option figures. A candidate requires to identify such figures.

EXAMPLE

1. You are given a figure (X) followed by four option figures (a), (b), (c) and (d) such that figure (X) is exactly embedded in one of them. Trace out the option figure which contains figure (X) as its part.

(a)                  (b)

(c)                  (d)

Explanation (c):

Option (c) exactly embeds the given figure (X) as its part.

So the correct option is (c).

FIGURE FORMATION

This section deals with the following types of problems:

I.           Formation of a Figure from its Segments: In such type of problems, all the parts that are required to form a figure are given. A candidate requires to identify the figure so formed out of the four options.

II.       Choosing a Pattern which has the same components as a given Pattern : In such type of problems, a pattern of several components is given. A pattern out of four options contains the same components. A candidate requires to choose such pattern.

III.         Rotation of a Figure: In such type of problems, a figure is given. A figure out of four options is the same figure as the given one, but this is obtained after rotating the given figure. A candidate requires to identify such figure.

2.   Find out which of the figures (a), (b), (c) and (d) can be formed from the pieces given in figure (X).

(a)                 (b)

(c)                 (d)

Explanation (c):

The option figure (c) contains all the parts of figure (X) as follows:

3.   Select the option in which all the components of the figure (X) are found.

(a)                 (b)

(c)                 (d)

Explanation (c):

Figures (a) and (b) do not have '+'. Figure (d) does not have (?), figure (c) has all the components of figure (X).

4.   Find out how the figure (X) look will like after rotation.

(a)                  (b)

(c)                  (d)

Explanation (c):

After rotating the given figure (X) clockwise through $90{}^\circ$, we get figure (c),

CONSTRUCTION OF SQUARES

Such type of problems are on the basis of the geometrical figures.

A candidate is required to identify the figure which can fit into each other to form a square.

5. Select a figure from the options which fits exactly into figure (X) to form a complete square.

(a)                 (b)

(c)                  (d)

Explanation: (b)

So, the correct option is (b).

GROUPING OF IDENTICAL FIGURES

In such type of problems a set of some figures is given. Usually these are four or six or nine in counting. These figures are numbered as 1, 2, 3, 4,...

A candidate requires to classify these figures into groups on the basis of some common properties amongst them.

6. Group the following figures into three classes regarding common properties amongst them.

(a) 1, 4, 6; 3, 7, 9; 2, 5, 8

(b) 2, 4, 6; 3, 5, 9; 1, 7, 8

(c) 3, 5, 8; 1, 2, 6; 4, 7, 9

(d) 4, 5, 9; 1, 2, 8; 3, 6, 7

Explanation (a):

1, 4, 6 are cup-shaped three dimensional figures.

3, 7, 9 are box type three-dimensional figures.

2, 5, 8 are simple two dimensional figures divided into halves.

So, the correct option is (a).

FIGURE MATRIX

In such type of problems a2x2or3x3 grid is given. This grid has some designs or symbols to form a pattern. But a cell of the grid is left empty.

A candidate is required to fill up the cell. For it one may analyse the grid and identify a rule along row-wise or column-wise in the grid.

7. Select a figure from the options that can replace the question mark(?) in order to complete the given figure matrix.

(a)                      (b)

(c)                       (d)

Explanation (a):

In each row, 1st figure rotates clockwise through $90{}^\circ$ to become 2nd figure.

And 2nd figure rotates through $180{}^\circ$ to become 3rd figure.

After rotatingthrough $180{}^\circ$, we getwhich is the required figure.

So the correct option is (a).

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