Measurement Formula

Quite often in the school students are doing the measurement activities. Such activities are heavily dependent on using various formulas. For example to measure the area of the rectangle we use the formula, A = L × B. We have to remember these formulas for the correct result of the measurements. In this topic, we will discuss how such a Measurement Formula will be used in Physics with some examples. Let us learn these formulas.

What are the Measurement Activities?

Measurement activities are used to measure something. It is the estimation of ratios of a certain quantity. It is made by comparing some quantity with the standard unit. These are used to find the size, length, area, perimeter, volume or amount of something. Measurement Formulas are used to find the distance, area, surface area, volume, circumference, density, mass, etc. Sometimes we are doing the conversions like conversion of an inch to feet, kilometer to miles, etc.

There are numerous formulas which we should be able to remember. But, most people cannot recall all of these formulas quickly. Also, many people can recall, but even they do not know when to use them or whether they have any relevance to their everyday life. More importantly, there are many occasions in our daily life when we even do not know the formulas to compute the measurement of some shape.

Some Important Formulas:

• Area of the rectangle, \(A = L \times B\)
• Area of the square, A\( =Side ^2\)
• Perimeter of a rectangle, \(P = 2 \times ( L+B )\)
• Perimeter of square, \(P = 4 \times Side\)
• Area of the triangle, \(A = \frac{1}{2} \times Base \times Height\)
• Circumference of a Circle, \(C = 2 \times \pi \times r\)
• Area of the circle, \(A = \pi \times r^2\)
• The surface area of a cube, \(S = 6 \times a^2\)
• The volume of a cube, \(V = a^3\)
• Surface area of a cuboid, \(S = 2\times (LB + BH +HL)\)
• Length of Diagonal of Cube \(d= \sqrt{3} a\)

Where,

A	Area of the shape
L	Length of the shape
B	The breadth of the shape
H	Height of the shape
P	The perimeter of the shape
C	Circumference of the circle
r	The radius of the circle
S	The surface area of the shape
a	Side of the Cube
V	The volume of the shape
d	Diagonal of the cube
\(\pi\)	Constant

Solved Examples for Measurement Formula

Q.1: Find the area of a triangle with a given base length of 3 cm and a height of 8 cm. Use the appropriate Measurement Formula.

Solution: Given values in the problem are,

Base  = 3 cm

Height = 8 cm

Then Area of the Triangle will be,

\(A = \frac {1}{2} Base \times Height \\\)

\(A = \frac {1}{2} 3 \times 8 \\\)

\(= 12 \;square \;cm\)

Thus area of the triangle will be 12 square meter.

Q.2: Find the area of the circle with a length of circumference as 44 cm.

Solution: First find the radius of the circle as,

\(C= 2 \times \pi \times r\)

Rearranging the formula,

\(r = \frac {C}{2\times \pi}\\\)

thus\( \; r = \frac{440}{2* \frac{22}{7}} \\\)

r = 7

Now, apply the formula to get the area of the circle as,

\(A = \pi \times r^2 \\\)

\(A  = \frac{22}{7}\times 7 \times 7 \\\)

\(=154 \;square \;cm.\)

The area of the circle will be 154 square meters.