How to Calculate and Solve for the Area, Base and Height of a Triangle | The Calculator Encyclopedia

The image above is a triangle.
To compute the area of a triangle two essential parameters are required which are the base of the triangle and the height of the triangle.

The formula for calculating the area of a triangle is:

A = 0.5bh

Where:

A = Area of a Triangle
b = Base of a Triangle
h = Height of a Triangle

Let’s solve an example:
Given that the base of a triangle is 12 cm and the height of the triangle is 4 cm. Find the area of the triangle.

This implies that:
b = Base of the Triangle = 12 cm
h = Height of the Triangle = 4 cm

A = 0.5bh
A = 0.5(12)(4)
A = 0.5(48)
A = 24

Therefore, the area of the triangle is 24 cm2

How to Calculate the Base of a Triangle when the Area and Height of the Triangle is Given

The formula is:

b = 2A / h

Where:

b = Base of the Triangle
A = Area of the Triangle
h = Height of the Triangle

Let’s take an example:
Find the base of a triangle when the height and area of the triangle is 12 cm and 40 cm2 respectively.

This implies that:
A = Area of the Triangle = 40 cm2
h = Height of the Triangle = 12 cm

b = 2(40) / 12
b = 80 / 12
b = 6.667

Therefore, the base of the triangle is 6.667 cm.

How to Calculate the Height of a Triangle when the Area and Base of the Triangle is Given

The formula is:

h = 2A / b

Where:

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How to Calculate and Solve for the Perimeter, Length and Width of a Rectangle | The Calculator Encyclopedia

The image above is a rectangle with a length of 8 cm and a width of 5 cm.
To compute the perimeter of a rectangle requires two parameters which are the length of the rectangle and the width of the rectangle.

The formula for calculating the perimeter of a rectangle is:

P = 2 (l + w)

Where:

P = Perimeter of a Rectangle
l = Length of a Rectangle
w = Width of a Rectangle

Let’s solve an example:
Find the perimeter of a rectangle where the length of the rectangle is 8 cm and the width of the rectangle is 5 cm.

This implies that:
l = Length of the Rectangle = 8 cm
w = Width of the Rectangle = 5 cm

P = 2 (l + w)
P = 2 (8 + 5)
P = 2 (13)
P = 26

Therefore, the perimeter of the rectangle is 26 cm.

How to Calculate the Length of a Rectangle when the Perimeter of the Rectangle and the Width of the Rectangle is Given

l = P / 2 – w

Where:
l = Length of the Rectangle
P = Perimeter of the Rectangle
w = Width of the Rectangle

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How to Calculate and Solve for the Area, Width and Length of a Rectangle | The Calculator Encyclopedia

The image above is a rectangle with a length of 9 cm and a width of 4 cm.
To compute the area of a rectangle requires two essential parameters which are the length of the rectangle and the width of the rectangle.

The formula for calculating the area of a rectangle is:

A = lw

Where:

A = Area of a Rectangle
l = Length of a Rectangle
w = Width of a Rectangle

Let’s solve an example
Find the area of a rectangle where the length of the rectangle is 9 cm and the width of the rectangle is 4 cm.

This implies that:
l = Length of the Rectangle = 9 cm
w = Width of the Rectangle = 4 cm

A = lw
A = (9)(4)
A = 36

Therefore, the area of the rectangle is 36 cm2.

How to Calculate the Length of a Rectangle when the Area and Width of the Rectangle is Given

The formula for calculating the length of the rectangle is:

l = A / w

Where:

l = Length of the Rectangle
A = Area of the Rectangle
w = Width of the Rectangle

Let’s solve an example:
Find the length of a rectangle where the area of the rectangle is 45 cm2 and the width of the rectangle is 9 cm.

This implies that:
A = Area of the Rectangle = 45 cm2
w = Width of the Rectangle = 9 cm

l = A / w
l = 45 / 9
l = 5

Therefore, the length of the rectangle is 5 cm.

How to Calculate the Width of a Rectangle when the Area and Length of the Rectangle is Given

The formula for calculating the width of the rectangle is:

w = A / l

Where:

w = Width of the Rectangle
A = Area of the Rectangle
l = Length of the Rectangle

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How to Calculate and Solve the Centre of Gravity of a Segment of a Sphere

The image above represents a segment of a sphere.
To compute the centre of gravity of a segment of a sphere requires two essential parameters. These parameters are the radius of the sphere and height of the segment of the sphere.

The formula for computing the centre of gravity of a sphere is:

C.G. = 3(2r – h)² / 4(3r – h)

Where:
C.G. = Centre of Gravity
r = Radius of the Sphere
h = Height of the Segment of the Sphere

Let’s solve an example
Find the centre of gravity of the segment of the sphere where the radius of the sphere is 10 m and the height of the segment of the sphere is 4 m.

This implies that:
r = Radius of the Sphere = 10
h = Height of the Segment of the Sphere = 4

C.G. = 3(2(10) – 4)² / 4(3(10) – 4)
C.G. = 3(20 – 4)² / 4(30 – 4)
C.G. = 3(16)² / 4(26)
C.G. = 3(256) / 104
C.G. = 768 / 104
C.G. = 7.38

Therefore, the centre of gravity of the segment of the sphere is 7.38.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a segment of a sphere at a height, h at a distance from the centre of the sphere measured along the height.

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How to Calculate and Solve for the Centre of Gravity of a Cube

The image above is a cube with a length of 5.2 cm.
To compute the centre of gravity of a cube, one essential parameter is needed and this parameter is the length of the cube (l).

The formula for calculating the centre of gravity of a cube is:

C.G. = 0.5(l)

Where:
l = Length of the Cube
C.G. = Centre of Gravity

Let’s solve an example:
Find the centre of gravity of a cube where the length of a side of the cube is 5.2 cm.

This implies that:
l = Length of the Cube = 5.2

Continue reading How to Calculate and Solve for the Centre of Gravity of a Cube

How to Calculate and Solve for the Centroid or Centre of Gravity of a Hemisphere

The image above is a hemisphere with a radius of 5.
To compute the centroid or centre of gravity of a hemisphere. You need one essential parameter and this parameter is the radius of the hemisphere (r).

The formula for calculating the centroid or centre of gravity of a hemisphere is:

C.G. = 3r / 8

Where
r = Radius of the hemisphere

As always let us try and solve an example:
Find the centroid or centre of gravity of a hemisphere where the radius is 5 cm.

From the formula this implies that:
r = Radius of the hemisphere = 5

C.G. = 3(5) / 8
C.G. = 15 / 8
C.G. = 1.875

Therefore, the centroid or centre of gravity of the hemisphere is 1.875.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a hemisphere at a distance from its base measured along the vertical radius.

To get the answer and workings of the center of gravity or centroid of a hemisphere using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

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Nickzom Calculator Calculates the Centroid or Centre of Gravity of a Semicircle | Statics (Mechanics)

The image above is a semicircle with a radius of 7 cm.
To compute the centroid or centre of gravity of a semicircle, you need one essential parameter and this parameter is the radius of the semicircle.

The formula for calculating the centroid or centre of gravity of a semicircle is:

C.G.= 4r /

Where:
r = Radius of the Semicircle
π = Mathematical Constant = 3.142 (approximately)

Let’s solve an example:
Find the centroid or centre of gravity of a semicircle where the radius is 7 cm.

From the example above,
r = radius of the semicircle = 7

C.G. = 4(7) /
C.G. = 28 / 9.4247
C.G. = 2.97

Therefore, the centroid or centre of gravity of the semicircle is 2.97.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a semicircle at a distance from its base measured along the vertical radius.

To get the answer and workings of the center of gravity or centroid of a semicircle using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

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How to Calculate and Solve for the Centroid or Centre of Gravity of a Sphere

The image above is a sphere and 18 m is the diameter of the sphere. In the computing of the centroid or centre of gravity of a sphere there is only one essential parameter which is the diameter of the sphere.

The formula for calculating the centroid or centre of gravity of a sphere is:

C.G. = d / 2

Where:

d is the diameter of the sphere

As always, let’s take an example:

Let’s solve an example
Find the centroid or centre of gravity of a sphere where the diameter is 18 m.

C.G. = 18 / 2
C.G. = 9

Therefore, the centroid or centre of gravity of the sphere is 9.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a sphere at a distance from every point.

To get the answer and workings of the center of gravity or centroid of a sphere using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

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How to Calculate and Solve the Centre of Gravity of a Right Circular Cone

This image above is a display of what a right circular cone looks like. There is only one essential parameter for calculating the centroid or centre of gravity of a right circular cone. This parameter is the height of the cone (h).

The formula for calculating the the centroid or centre of gravity of a right circular cone is:

C.G. = h / 4

As always let’s solve an example.

Find the centroid or centre of gravity of a right circular cone where the height of the cone is 12cm.
This implies that:

h = height of the cone = 12

C.G. = 12 / 4
C.G. = 3

Therefore, the centroid or centre of gravity of the right circular cone is 3.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a right circular cone at a distance from its base measured along the vertical axis.

To get the answer and workings to center of gravity or centroid of a right circular cone using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

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How to Calculate the Centre of Gravity of a Circular Sector in Statics | Mechanics

It is very possible to compute the centroid or centre of gravity of a circular sector. There are two highly important parameters one needs to know to compute the centre of gravity of a circular sector. These parameters are:

  • Radius of the Sector (r)
  • Semi Vertical Angle (α)

The formula for computing the centre of gravity of a circular sector is:

C.G. = 2rsinα /

Now, let’s take an example.
Let’s find the centroid or the centre of gravity of a circular sector that has a radius of 4m and a semi vertical angle of 30°.
This implies that:

r = Radius of the Sector = 4
α = Semi Vertical Angle = 30

Entering this values into the formula we have:

C.G. = 2(4)sin30° / 3(30)
C.G. = 8 . sin30° / 90
C.G. = 8 . (0.5) / 90
C.G. = 4 / 90
C.G. = 0.0444

Therefore, the centroid or centre of gravity of the circular sector is 0.0444.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a circular sector making a semi vertical angle α at a distance from the centre of the sector measured along the central axis.

To get the answer and workings to center of gravity or centroid of a circular sector. First, you need to obtain the Nickzom Calculator – The Calculator Encyclopedia app.

Continue reading How to Calculate the Centre of Gravity of a Circular Sector in Statics | Mechanics