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 Area, Length and Height of a Trapezium | The Calculator Encyclopedia

The image above is a Trapezium

To compute the area of a trapezium, three essential parameter is needed and they are the length of the top side (a), length of the bottom side (b) and the height of the trapezium (h).

The formula for calculating the area of a trapezium is;

A = 0.5[a + b]h

Where;
A = Area of a trapezium
a = length of the top side of the trapezium
b = length of the bottom side of the trapezium
h = height of the trapezium

Let’s solve an example;
Find the area of a trapezium where length of top side (a) is 7 cm, length of bottom side (b) is 12 cm and height of trapezium (h) is 10 cm.

This implies that;
a = Length of top side of the trapezium = 7 cm
b = Length of bottom side of the trapezium = 12 cm
h = Height of the trapezium = 10 cm

A = 0.5[a + b]h
A = 0.5[7 + 12]10
A = 0.5[19]10
A = 95

Therefore, the area of a trapezium is 95 cm2

How to Calculate the Height of a Trapezium when the Area, Length of top side and Length of bottom side of the Trapezium is given.

The formula is h = A / 0.5(a + b)

Where;
A = Area of the trapezium
a = Length of the top side of the trapezium
b = Length of the bottom side of the trapezium

Let’s solve for an example;
Given that the length of top side (a) is 10 cm, length of bottom side (b) is 14 cm and the area of the trapezium is 20 cm2 Find the height of the trapezium?

This implies that;

A = Area of the trapezium = 20 cm2
a = Length of top side of the trapezium = 10 cm
b = Length of bottom side of the trapezium = 14 cm

h = A / 0.5(a + b)
h = 20 / 0.5(10 + 14)
h = 20 / 0.5(24)
h = 20 / 12
h = 1.667

Therefore, the height of the trapezium is 1.667 cm.

Continue reading How to Calculate and Solve for the Area, Length and Height of a Trapezium | The Calculator Encyclopedia

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

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

How to Calculate and Solve for the Area and Length of a Square | The Calculator Encyclopedia

The image above represents a square.
To compute the area of a square requires one essential parameter which is the length of one side of a square.

The formula for computing the area of a square is:

A = l2

Where:
A = Area of a Square
l = Length of one side of a Square

Let’s solve an example
Find the area of a square which has a length of 6 ft.

This implies that:
l = length of one side of a square = 6

A = l2
A = 62
A = 6 x 6
A = 36

Therefore, the area of the square is 36 ft2.

Calculating the Length of a Square when Area is Given

The formula is l = √[A]

Where;
A = Area of a square
l = Length of a square

Let’s solve an example:
Find the length of a square where the area of a square is 81 ft2.

This implies that;
A = Area of a square = 81 ft2

l = √[A]
l = √[81]
l = 9

Therefore, the length of the square is 9 ft.

Continue reading How to Calculate and Solve for the Area and Length of a Square | The Calculator Encyclopedia

How To Calculate and Solve for the Area, Radius and Diameter of a Circle | The Calculator Encyclopedia

The image above is a circle.

To compute the area of a circle, one essential parameter is needed and this parameter is the radius of a circle (r). You can also use the diameter of a circle to compute the area of a circle (d).

The formula for calculating the area of a circle is:

A = πr2

Where:

A = Area of a circle
r = Radius of a circle

Let’s solve an example:
Find the area of a circle where the radius of a circle is 6 cm.

This implies that;
r = Radius of a circle = 6 cm

A = πr2
A = 3.142 (6)2
A = 3.142 (36)
A = 113.10

Therefore, the area of a circle is 113.10 cm2

Calculating the Area of a Circle using the Diameter of a Circle.

The formula is A = πd2/4

Where;
A = Area of a circle
d = Diameter of a circle

Let’s solve an example:
Find the area of a circle where the diameter of the circle is 7 cm.

This implies that;
d = Diameter of a circle = 4 cm

A = πd2 / 4
A = 3.142 (4)2 / 4
A = 3.142 (16) / 4
A = 3.142 (4)
A = 12.57

Therefore, the area of a circle with diameter given is 12.57 cm2

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How to Calculate and Solve for Linear Expansivity, Area Expansivity and Volume or Cubic Expansivity

Linear expansivity, area expansivity and volume or cubic expansivity are all parameters that are being governed by heat energy. All three parameter is dependent on temperature rise which is primarily in Celsius unit of temperature.

Linear expansivity additionally depends on the original length and final length, area expansivity additionally depends on the original area and final area and lastly, cubic or volume expansivity depends on the original volume and final volume.

The formula for calculating linear expansivity is (l2 – l1) / l1θ
l2 represents the final length.
l1 represents the original length.
θ represents the temperature rise in Celsius.

The formula for calculating area expansivity is (A2 – A1) / A1θ
A2 represents the final area.
A1 represents the original area.
θ represents the temperature rise in Celsius.

The formula for calculating volume or cubic expansivity is (V2 – V1) / V1θ
V2 represents the final volume.
V1 represents the original volume.
θ represents the temperature rise in Celsius.

Continue reading How to Calculate and Solve for Linear Expansivity, Area Expansivity and Volume or Cubic Expansivity