Solving Online Geometry Tests

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.

 

Problems on solving online geometry tests:

 

Example problem 1:

 If the area of a parallelogram is 180 mm2 and the height is 9 mm, what is the length of the base?

Solution:

Area of the parallelogram=180 mm2

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 = 2x.

4x to 2x reduces to 4 to 2.

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

By solving this,

6x = 180°

x = 30°

Then, 4x = 4(30°) and 2x = 2(30°).

So, 4x = 120° and 2x = 60°

The angles have measures of 120° and 60°.

 

 

Few more problems on solving online geometry tests

 

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*r2 h

By solving this,

v=(22/7)*(7/2)*(7/2)*40=1540 cm3

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 cm2.

The area of the trapezium ABCG = 21 (36 + 28) × 14 = 64 × 7 = 448 cm2.

The area of the semi-circle DEF = 21 × 722 × 14 × 14 = 22 × 14 = 308 cm2