**Basic Geometry - Area Formulas**

- Area of a Rectangle = Base × Height.
- Area of a Square = Base × Height.
- Area of a Square = s
^{2} - Area of Triangle = ½(Base × Height)
- Area of Parallelogram = Base × Height.
- Area of Trapezoid = ½(Base
_{1}+ Base_{2}) × Height. - Area of Circle = π(radius)
^{2}= πr^{2}

**Volume = (l x b x h) cubic units**. Surface area = 2(lb + bh + lh) sq. units.

Question. What is meant by mensuration? Answer. Mensuration refers to the branch of mathematics which involves **the study of various geometrical shapes**. Furthermore, it deals with the areas and Volume of such geometrical figures.

The surface area of any given object is the area or region occupied by the surface of the object. Whereas **volume is the amount of space available in an object**. In geometry, there are different shapes and sizes such as sphere, cube, cuboid, cone, cylinder, etc. Each shape has its surface area as well as volume.

What are the formulas of cylinder? The formulas of cylinder are: **Total surface area = 2πr(r+h) square units**. Volume of cylinder = πr^{2}h cubic units.

Next, determine the mass of the liquid through a table lookup. For water density, this would be approx. 997 kg/m^3. Finally, calculate the liquid volume using the formula **LV = M/d**.

**Basic Geometry - Area Formulas**

- Area of a Rectangle = Base × Height.
- Area of a Square = Base × Height.
- Area of a Square = s
^{2} - Area of Triangle = ½(Base × Height)
- Area of Parallelogram = Base × Height.
- Area of Trapezoid = ½(Base
_{1}+ Base_{2}) × Height. - Area of Circle = π(radius)
^{2}= πr^{2}

A cylinder consists of two types of surface, one is a curved surface and the other is a circular basis. The area of both circular bases is equal. The Surface Area of the Cylinder can be Classified into Two Types: **Curved surface area (CSA)** **Total surface area (TSA)**

What is the formula of surface area and volume?

Shape | Total Surface Area | Volume formula |
---|---|---|

Cuboid | 2(lb+bh+hl) Where, l = length, b = breadth and h = height | Length x Width x Height |

Prism | ph+2B Where p= perimeter of the base, h = height and B =area of the base | Area of base x Height |

Volume of Cube = **√3 × d ^{3}/9**

Hence, by measuring the length of the diagonal of cube, we can evaluate the volume of cube. Example: If length of diagonal of cube is 3 inches, then the volume will be: Volume = √3 × d

Mensuration is **a division of mathematics that studies geometric figure calculation and its parameters such as area, length, volume, lateral surface area, surface area, etc**. It outlines the principles of calculation and discusses all the essential equations and properties of various geometric shapes and figures.

Once you know both the density and the mass, **divide the mass by the density** to find the volume. If you want to calculate volume in milliliters, measure the weight in grams.

Ans: Two types of mensuration are **2D and 3D mensuration**. Mensuration applies to two-dimensional (2D) figures like squares, rectangles, triangles, parallelograms, trapezium, etc. It applies to three-dimensional (3D) figures like a cube, cuboid, cylinder, cone, sphere, etc.

**Surface Areas And Volumes**

- To find the surface area of a solid, add the areas of all the faces. You can remember the formula as sum of areas of the all the faces. For example: For Cube.
- Volume of a pyramid is one third of area of its base times height. For Example:

**Multiply the length and width, or c and b to find their area**. Multiply this measurement by two to account for both sides. Add the three separate measurements together. Because surface area is the total area of all of the faces of an object, the final step is to add all of the individually calculated areas together.

V=πr2h

Volume is the measure of the 3-dimensional space occupied by matter, or enclosed by a surface, measured in cubic units. The SI unit of volume is the **cubic meter (m ^{3})**, which is a derived unit. Liter (L) is a special name for the cubic decimeter (dm

Calculate the volume of the substance by dividing the mass of the substance by the density (**volume = mass/density**).

The formula for density is the mass of an object divided by its volume. In equation form, that's **d = m/v** , where d is the density, m is the mass and v is the volume of the object. The standard units are kg/m³.

Surface Area Formulas

Find the area of each face. Add up all areas. **SA=2B+2πrh**. Find the area of the base, times 2, then add the areas to the areas of the rectangle, which is the circumference times the height. SA=4πr2.

Dated : 13-May-2022

Category : Education