**Introduction :**

Geometry is a part of math which involves the study of shapes, lines, angles, dimensions, etc. it plays vital role in real time application like elevation, projection. Online learning of geometry gives many fundamental skills and helps to build the lateral thinking, deductive reasoning, and analytical reasoning and testing. Lines, circles and triangles are called the Plane Geometry.Three-dimensional shapes like spheres and cubes are called Solid geometry. Now, we are going to see some of the solving online geometry test problems.

**Example problem 1:**

If the area of a parallelogram is 180 mm^{2} and the height is 9 mm, what is the length of the base?

**Solution:**

Area of the parallelogram=180 mm^{2}

Formula for the area of parallelogram= base *height

180=base*9

By solving this,

Base=180/9=20 mm.

So, the base of the parallelogram is 20 mm.

**Example problem 2:**

The ratio of two supplementary angles is 4 to 2. Find the measure of each angle.

**Solution:**

Let measure of smaller angle = *4x,* measure of larger angle = 2*x.*

*4**x* to 2*x* reduces to 4 to 2.

*4**x* + 2*x* = 180*°* (The sum of supplementary angles is 180*°*.)

By solving this,

*6x* = 180*°*

*x* = 30*°*

Then, 4*x* = 4(30*°*) and 2*x* = 2(30*°*).

So, *4x* = 120*°* and 2*x* = 60*°*

The angles have measures of 120*°* and 60*°*.

**Example problem 3:**

The base of a right circular cylinder diameter is 7 cm. If its height is 40 cm, find its volume.

**Solution :**

Since the diameter of the base is 7 cm, its radius *r* = cm. Also, *h* = 40 cm,

and pi=22/7.. Therefore, the volume of the cylinder is given by

V = Pi*r^{2} *h*

*By solving this,*

*v*=(22/7)*(7/2)*(7/2)*40=1540 cm^{3}

**Example problem 4:**

Find the area enclosed by Figure:

**Solution:**

The figure is the combination of the rectangle *CDFG*, the semi circle *DEF* and the trapezium *ABCG*.

The area of the rectangle *CDFG* = 28 × 13 = 364 cm^{2}.

The area of the trapezium *ABCG* = 21 (36 + 28) × 14 = 64 × 7 = 448 cm^{2}.

The area of the semi-circle *DEF* = 21 × 722 × 14 × 14 = 22 × 14 = 308 cm^{2}