In mathematics, the area that studies shapes, sizes, properties of space, and the relative position of figures is known as geometry. People back then used geometry formulas to calculate length, area, and volume. The advanced geometry is divided into two categories or groups i.e., plane geometry and solid geometry. Different shapes like triangle, circle, square, rectangle, etc are part of plane geometry. On the other hand, the calculations of the perimeter, area, length, and volume of different geometric figures and shapes are under solid geometry. What concerns the students studying geometry is the geometrical formula. Geometry is a thing that we use every day in life so its formulas form the foundation of it and it is very important to know them.

To solve the geometrical problems easily we need to know the formulas so here we are, the formulas of the important geometrical shapes are given below.

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The Perimeter of a Square: 4 x side

The Area of a Square: side × side = side2

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The Perimeter of a Rectangle: 2 x (length + width) square unit

The Area of a Rectangle: length x width

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The Diameter of a Circle: 2 × r

Circumference of a Circle: 2 × π × r

Area of a Circle: π × r2

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We can find the area and the perimeter of a triangle using the formula:

The Perimeter of a Triangle: side a + side b + side c

The Area of a Triangle: ½ x base of the triangle x height of the triangle.

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The Total surface area of Cube: 6a2 in a square unit

The Volume of a Cube: a3 cubic unit

The Perimeter of a Cuboid: 4 x (length + breadth + height)

The Total surface of a Cuboid: 2 x [(length x breadth) + (breadth x height) + (length x height)]

The Volume of a Cuboid: length x breadth x height

The Total surface area of a Right Prism: the perimeter of the base x height + 2 x area of the base

The Volume of a Right Prism: area of the base x height

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The Total surface area of the Right Circular Cylinder: 2 π r (h + r) square units

The Volume of the Right Circular Cylinder: πr2h

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The Total surface area of a Pyramid: base area + ½ (number of the sides of the base x slant height x base length)

The volume of a Pyramid: ⅓ x base area x height

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The Total surface area of a Right Circular Cone: π(r + l) r

The Volume of a Right Circular Cone: 1/3 πr2h

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**The Diameter of a Sphere:** 2 r

**The Surface area of a Sphere: **4 πr2

**The Volume of a Sphere: **(4 ⁄ 3) πr3

Example 1) If the sides of a polygon are 5 cm, 4 cm, and 2 cm, find the perimeter.

Solution 1) a = 5 cm, b = 4 cm, and c = 2 cm

Perimeter = a + b + c

= 5 + 4 + 2

= 11 cm

Example 2) What will be the circumference of a circle if its radius is 7 cm?

Solution 2) Using the formula 2πr

Substituting it 2 x (22/7) x 7

22 x 7

154 cm2

FAQ (Frequently Asked Questions)

Question 1) What is a Right Prism?

Answer 1) A prism is a solid that is usually bounded by a number of plane faces. Two of its faces are congruent parallel polygons known as the ends and other faces are called the side faces (or lateral faces), which are parallelograms. A right prism is the one where the side-edges of it are perpendicular to its ends (or to base), otherwise, it will be called an oblique prism.

In the right prism, the side faces of it are all rectangles and each side-edge of it is equal to its height.

Question 2) What is a Right Circular Cylinder?

Answer 2) A right circular cylinder is one that has a closed circular surface that has two plane parallel bases on both the ends. The elements of a right circular cylinder are perpendicular to its base. We can also call it the right cylinder. In the right cylinder, all the points lie on the closed circular surface which is at a fixed distance from a straight line called the axis of the cylinder. The two circular bases of the right cylinder are of the same radius and are parallel to each other.

Question 3) What is the difference between a Cone and a Pyramid?

Answer 3) A right circular cone is one where the axis of the cone is the line that meets the vertex to the midpoint of the circular base. In other words, the center point of the circular base of a cone is joined with the apex and it forms a right angle. A cone is a 3d shape that has a circular base and narrows smoothly to a point just above the base. We call this point an apex. On the other hand, a pyramid is a polyhedron having a polygonal base and the sides are triangular. It has three main parts: apex, face, and base. In a pyramid, the base can be of any shape but the faces usually take an isosceles triangular shape. All the triangular sides meet at a point on the top of the pyramid that is known as the “Apex”.

Question 4) What is the difference between a Square, Rectangle, Cube, and Cuboid?

Answer 4) The difference between the four are:

Square | Rectangle | Cube | Cuboid |

A square is a two-dimensional quadrilateral that has 4 sides and 4 angles and all the four angles of a square are 90 degrees. | A rectangle also has 4 sides and 4 angles just like a square but the only point of difference between them is that in a square all the sides are equal but in a rectangle only the opposite side is equal. | Cube is a three-dimensional regular hexahedron figure that has 6 square faces, 8 vertices, and 12 edges. | A cuboid, just like a cube is a 3d shape having six, rectangle-shaped sides. Cuboid also has eight vertices (corners) and twelve edges. The angles in a cuboid are all right angles. |