Solve Maths Formula

Mathematics is an interesting subject compare to other subjects. Mathematics subject applies from kids school to college students. Math has various sections to deal different things for real life. Math subject is used for many real life applications.

In math, we have many interesting chapters. They are numbers, algebra, geometry, trigonometry, matrices, probability, statistics, and calculus.

In every math chapter, it has own formulas to solve problems. In this article, we see about solving some chapter problems using formulas.

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Some Math formulas:

Algebra Formulas:

(a - b)2 = a2 - 2ab + b2

(a2 – b2) = (a + b)(a – b)

a * (b + c) = a * b + a * c

Mid-Point Formula:

Mid Point = ( `(x_1+x_2)/2 , (y_1+y_2)/2` )

Geometry Formulas:

Parallelogram:

Area = base x height

Perimeter = 2 x (Side 1 + Side 2)

Rhombus:

Area = Base x Height

Perimeter = 4 x side

Rectangular Prism:

Surface area = 2(Length x Width + Width x Height + Length x Height)

Volume = Length x Width x Height

Sphere:

Surface area = 4 x `pi` x Radius2

Volume = `4/3` x `pi` x Radius3

Trigonometry formulas:

Sin A = Opposite Side / Hypotenuse

Cos A = Adjacent side / Hypotenuse

Tan A = Opposite side / Adjacent side

Let us see some example problems using formulas.

Example problems using Math formulas:

Problem 1:

Simplify the expression: 2 x (2m + 4n) = (2m - 4n)2

Solution:

We can simplify this using following formula.

a x (b + c) = ab + ac

(a - b)2 = a2 - 2ab + b2

2 x 2m + 2 x 4n = 4m2 - 16mn + 16n2

4m + 8n = 4m2 - 16mn + 16n2

Group all variables in one side

4m2 - 16mn - 4m - 8n + 16n2 = 0

Thus the simplified expression, 4m2 - 16mn - 4m - 8n + 16n2 = 0

Problem 2:

Solve the mid point for the given two points: (5 , 7) and (9 , 10)

Solution:

We can solve the mid point by using mid point formula.

Mid Point  = ( `(x_1+x_2)/2 , (y_1+y_2)/2` )

Given:

(x1 , y1) = (5 , 7)

(x2 , y2) = (9 , 10)

Mid point = ( `(5+9)/2 , (7+10)/2` )

Mid point = (7 , 8.5)

Therefore, Mid point of this two given points is (7 , 8.5)

Problem 3:

What is the area and Perimeter of Parallelogram for the base is 6 meter and height is 8 meter. Another side length of parallelogram is 10 meter.

Solution:

Formula:

Area = base x height

Solve area,

Area = 6 x 8

Area = 48 square cm.

Formula:

Perimeter = 2 x (side 1 + side 2)

Solve for perimeter,

Perimeter = 2 x (6 + 10)

Perimeter = 2 x (16)

Perimeter = 32 cm.

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Problem 4:

In a right triangle ABC, opposite length is 6 m and Hypotenuse length is 8 m. Find the angle A.

Solution:

We can find angle using trigonometry function formula.

Opposite = 6 m

Hypotenuse = 8 m

Formula is Sin A = Opposite side / Hypotenuse

Solve for angle A,

Sin A = `6/8`

Sin A = 0.75

Take inverse sin both sides.

A = 48.6

Therefore, Angle A = 48.6°.