Subscribe to our YouTube channel for the latest videos, updates, and tips.


Formulas for 3D Shapes

Some of the useful math geometry formulas for 3D shapes are discussed below.

(i) Area of a Triangle: Let ABC be any triangle. If AD be perpendicular to BC and BC = a, CA = b, AB = c then the area of the triangle ABC (to be denoted by ⊿) is given by,

area of a triangle


⊿ = ¹/₂ × base × altitude. 

= ¹/₂ ∙ BC ∙ AD 

(b) ⊿ = √[s(s - a)(s - b)(s - c)] 

Where 2x = a + b + c = perimeter of the ⊿ ABC. 

(c) If the a be the length of a side of an equilateral triangle then its height = (√3/2) a and it’s area = (√3/4) a²

(ii) If a be the length and b, the breadth of a rectangle then its area = a ∙ b, length of its diagonal = √(a² + b² ) and its perimeter = 2 ( a + b). 


(iii) If a be the length of a side of a square, then its area = a² length of its diagonal = a√2 and perimeter = 4a.


(iv) If the lengths of two diagonals of a rhombus be a and b respectively then its area = (1/2) ab and length of a side = (1/2) √(a² + b²)


(v) If a and b be the lengths of two parallel sides of a trapezium and h be the distance between the parallel sides then the area of the trapezium = (1/2) (a + b) ∙ h.


(vi) Area of a Regular Polygon: The area of a regular polygon of n sides = (na²/4) cot (π/n) where a is the length of a side of the polygon. In particular, if a be the length of a side of a regular hexagon then its area

= (6a²/4) ∙ cot (π/6) = (3√3/2) ∙ a²


(vii) The length of circumference of a circle of radius r is 2πr and
its area = πr²


(viii) Rectangular Parallelopiped: If a, b and c be the length, breadth and height respectively of a rectangular parallelopiped then,

Rectangular Parallelopiped


(a) the area of its surfaces = 2 ( ab + bc + ca) 

(b) its volume = abc and 

(c) the length of diagonal = √(a² + b² + c² ).


(ix) Cube: If the length of the side of a cube be a then,

Cube surface area


(a) the area of its surfaces = 6a²,

(b) its volume = a³ and

(c) the length of the diagonal = √3a.


(x) Cylinder: Let r (= OA) be the radius of the base and h (=OB) be the height of a right circular cylinder ; then

curved surface area of a cylinder


(a) area of its curved surface = perimeter of base × height = 2πrh

(b) area of the whole surface = area of its curved surface + 2 × area of circular base
                                                = 2πrh + 2πr²
                                                = 2πr(h + r)

(c) volume of cylinder = area of base × height
                                    = πr²h


(xi) Cone: Let r (= OA) be the radius of the base, h (= OB), the height and I, the slant height of a right circular cone ; then

curved surface area of a cone


(a) l² = h² + r²

(b) area of its curved surface

= (1/2) × perimeter of the base × slant height = (1/2)∙ 2πr ∙ l = πrl

(c) area of its whole surface = area of the curved surface + area of the circular base

= πrl + πr² = πrl + πr(l + r).

(d) volume of the cone = (1/3) × area of the base × height = (1/3)πr²h

 Mensuration



11 and 12 Grade Math 

From Formulas for 3D Shapes to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 8 Times Table | Multiplication Table of 8 | Read Eight Times Table

    May 18, 25 04:33 PM

    Printable eight times table
    In 8 times table we will memorize the multiplication table. Printable multiplication table is also available for the homeschoolers. 8 × 0 = 0 8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40

    Read More

  2. Worksheet on Average | Word Problem on Average | Questions on Average

    May 17, 25 05:37 PM

    In worksheet on average interest we will solve 10 different types of question. Find the average of first 10 prime numbers. The average height of a family of five is 150 cm. If the heights of 4 family

    Read More

  3. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  4. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  5. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More