**Introduction to problems in geometry learning:**

Geometry is a powerful and fundamental branch in mathematics. The term ‘Geometry’ is the English word corresponding to the Greek word ‘Geometron’. Here Geo’ means Earth and ‘metron’ means Measurement.

Geometrical ideas had developed in all fields of art, measurements, architecture, engineering, cloth designing etc. In earlier, geometry was a group of related principles, which identify the areas, perimeters, lengths, volumes, and angles.

**Example 1:**

Determine the slope of the line whose equation is x + 2y = 4 .

**Geometry solution:**

The slope intercept form, y = mx + b

x + 2y = 4

2y = 4 - x

2y = -x + 4

y = (-x + 4)/2

y = (-1/2) x + 4/2

y = (-1/2) x+2

**m** **= -1/2**

**Example 2:**

Determine the x-intercept, the y-intercept, and the slope to the following equation..

5x + 2y = 10

**Geometry solution:**

The slope intercept form, y= mx +b

Here m-slope

b –y intercept

5x+2y=10

2y =10-5x

2y =-5x+10

y = (-5/2) x+10/2

y= (-5/2) x+5

**X-intercept = 2**

**Y-intercept = 5**

** Slope = 2.5**

John wants to decorate her Christmas tree. He wants to place the tree on a greeting box covered with colored paper with picture of Santa Claus on it. (He must know the exact quantity of paper buying for this purpose. If the box has length, breadth and height as 60 cm, 30 cm and 20 cm respectively how many square sheets of paper of side 30 cm would he require?

**Geometry solution:**

Since John wants to paste the paper on the outer surface of the box, the quantity of paper required would be equal to the surface area of the box, which is of the shape of a cuboid. The dimensions of the box are:

Length =60 cm, Breadth = 30 cm, Height = 20 cm.

The surface area of the box = 2(*lb* + *bh* + *hl*)

= 2[(60 × 30) + (30 × 20) + (20 × 60)] cm^{2}

= 2(1800 + 600 + 1200) cm^{2}

= 2 × 3600 cm^{2} = 7200 cm^{2}

The area of each sheet of the paper =30 × 30 cm^{2}

= 900 cm^{2}