Solve Geometry Exam

Introduction to solve geometry exam:

Geometry is a branch of mathematics that can be deals with the size, shape, position of shapes, and the properties of space. The geometry is also deals with the applications such as surveying, measurements, areas, and volumes. In Theoretical geometry or pure geometry, we give proofs for theorems on the properties of geometrical figures by applying axioms and reasoning. In practical geometry, we do not construct exactly the geometrical figures but draw rough sketches of the figures to give support to our logical reasoning. I like to share this Quadrilateral Formula with you all through my article.


Example problems to solve geometry exam:


Example problems to solve geometry exam are as follows:

1) The side length of cube is 10 cm. Find the volume of the cube.

Solution:

Formula for volume of the cube = a^3.
a= side length of the cube.

a=10 cm.

= (10)^3.

Volume of the cube =1000 cm^3.
This is the solution for the given geometry problem.


2)A triangle has a perimeter of 56. If 2 of its sides are equal and the third side is 8 more than the equal sides, what is the length of the third side?

Solution:

Let y = length of the equal side


Perimeter = sum of three sides.
Plug in the values from the question.
56 = y + y + y + 8

Combine like terms
56 = 3y + 8

3y = 56 – 8 (by equating the given equation)
3y = 48
y =16

Note: the third side is 5 more than the equal sides.

So, the length of third side = 16 + 8 =24

Answer: The length of third side is 24



Additional problems to solve geometry exam:


Additional problems to solve geometry exam are as follows:

1)The ratio of two supplementary angles is 12 to 6. Find the measure of each angle.

Solution:

Let measure of smaller angle = 12x, measure of larger angle = 6x.
12x + 6x = 180° (The sum of supplementary angles is 180°.)

18x = 180°

x = 10°
Then, 12x = 12(10°) and 6x = 6(10°).

So, 12x = 120° and 6x = 60° (by equating the given equation)

The angles have measures of 120° and 60°.
This is the solution for the given geometry example problem.

Geometry Terms and Definitions

Introduction to learning geometry terms and definitions:
Geometry is a branch of mathematics which  deals with the study of different shapes. Also learning the geometry terms and definitions include certain constructions of geometry such as lines, angles, plane etc., the word geometry is derived from the two words ‘geo’ meaning ‘earth’ and ‘metron’ meaning measuring. The geometry of plane figures are known as Euclidian geometry or plane geometry. I like to share this Skew Lines Examples with you all through my article.


Learning Terms and definitions of geometry:


There are various terms and definitions involved in geometry. Some of the terms and definitions involved in geometry for learning are listed below:

1. Point:

In geometry a point is a location in space with a dot on a piece of paper is known as point.

2. Mid point:

A segment that can be divides into two with equal length are known as mid point.

3. Square:

It has all the sides are equal with angles are equal to 90°. Then their diagonals are equal and they bisect at right angles.

4. Line:

The region where two points connects via the shortest path and continues indefintely in both the directions is referred as a line.

5. Line segments:

In geometry a line segments is a part of a line between the two points.

6. Perpendicular line segments:

If a line segments that intersect or cross at an angle of 90°. Then is it known as perpendicular line segments.

7. Parallel line segments:

If a line segments that never intersect or they can always in the same distance apart is known as parallel line segments.

8. Parallelogram:

The opposite sides are equal and parallel and opposite angles are equal. The diagonals are bisect to each other. Understanding Volume of Rectangular Prism is always challenging for me but thanks to all math help websites to help me out.


Learning terms and definitions of geometry for triangles and circles:


Learning terms and definitions of geometry for triangles and circles includes the following:

1. Right angle:

Angle that measures 90° is referred as right angle

2. Rectangle:

Their opposite sides are equal and parallel with the angles are equal to 90°..

3. Acute angle:

Angle that measures less than 90° is referred as acute angle

4. Obtuse angle:

An angle that measures more than 90° is referred as Obtuse angle.

5. Isosceles triangle:

A triangle with two equal length sides and also with two equal internal angles is referred as an isosceles triangle.

6. Equilateral triangle:

If a triangle has the equal length on all three sides, then it is referred as equilateral triangle.

7. Circles:

A circle has a locus of all points which equidistant from the center of a point.

8. Circumference:

The distance around a circle is called the circumference of a circle.

9. Concentric circles:

If the circles having the same centre but different radii are called concentric circles.

10. Tangent of circle:

If a line perpendicular to the radius, then, it can touches only one point on the circle.

Geometry Tests

Introduction:

Geometry is a part of mathematics. It used to calculate the measurements of angles, lines, surfaces and solid shapes. Geometry is using for depicting all kinds of shapes and their properties. Please express your views of this topic Tangent Line Problem by commenting on blog.

There are two main classifications in Geometry.

1) Plane Geometry

2) Solid Geometry


Example problems:


Problem 1: Find the volume of cone with radius 6 cm and height 10 cm.

Solution:

Given: Radius = 6 cm

Height = 10 cm.

Volume of cone = `(1/3)` * ` pi` * radius2 * height

= `(1/3)` * 3.14 * 62 * 10

= 0.33 * 3.14 * 36 *10

= 373.032 cubic cm.

The volume of cone is 373.032 cubic cm

Problem 2: Find the Perimeter of Parallelogram for the side a is 5 and side b is 9.

Solution:

Given: Side a = 5

Side b = 6

Perimeter of Parallelogram P = (2 * 5) + (2 * 9)

P = 10 + 18

P = 28

The Perimeter of Parallelogram is 28


Problem 3: Find the circle area and circumference radius with 6 cm.

Solution:

Given: Radius = 9 cm

Area of Circle = `pi ` * radius2

= 3.14 * 62

= 3.14 * 36

= 113.04 square cm.

The Area of Circle is 113.04 square cm

Circumference of Circle = 2 * `pi` * radius

= 2 * 3.14 * 9

= 37.68 cm

The circumference of circle 37.68 cm

Problem 4: Find the Area of triangle with height 3 cm and Base 4 cm.

Solution:

Given: Height = 3 cm

Base = 4 cm

Area of Triangle = (1/2) * height * base

= 0.5 * 3* 4

= 6 square cm

The Area of Triangle 6 square cm

Problem 5: Find the Area of Triangle with height 10 cm and Base 12 cm.

Solution:

Given: Height = 10 cm

Base = 12 cm

Area of Triangle =(1/2) * height * base

= 0.5 * 10* 12

= 60 square cm

The Area of Triangle =  60 square cm

Problem 6: Find the Perimeter of Parallelogram of  the side a is 7 and side b is 8.

Solution:

Given: Side a = 7

Side b = 8

Perimeter of Parallelogram P = (2 * 7) + (2 * 8)

P = 14 + 16

P = 30

The Perimeter of Parallelogram = 30

Problem 7: Find the circle area and circumference radius with 7 cm.

Solution:

Given: Radius = 9 cm

Area of Circle = π * radius2

= 3.14 * 72

= 3.14 * 49

= 153.86 square cm

The area of circle 153.86 square cm

Circumference of Circle = 2 * π * radius

= 2 * 3.14 * 7

= 43.96 cm

The Circumference of Circle = 43.96 cm