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# Area Volume and Points on a Grid

Area is a region bounded by a closed curve. Volume is a three-dimensional space a substance (solid, liquid, gas, or plasma) or shape and is expressed using SI unit, the cubic meter. A point on grid represents a point where it acts i.e. in 2D or 3D coordinate plane the point represents set vertices.

Similar Figures

Similar figures have the same shape but not the same size and the corresponding sides are proportional. That is, the ratios of the corresponding sides are equal. Similarly corresponding angles are equal.

The above 2 figures are said to be similar figures.

## Congruent Figures

Two polygons are congruent if they are the same size and shape i.e., if their corresponding angles and sides are equal.

The above 2 figures are said to be congruent figures.

Symmetric Figures:

A figure is said to be symmetric if it can be cut into identical pieces, and each being of the same dimensions.

## Perimeter, Area and Volume Facts

Perimeter is defined as the distance around a figure.

Perimeter of a rectangle is 2(l+b) metres, where l is the length and b is the breadth.

Perimeter of a square is 4a units where a is the length of the side.

Area of rectangle is l x b units2.

Area of square is a x a units2.

The space occupied by an object is called volume.

Volume of a cube is l x w x h units3.

Area And Perimeter Of Rectangle:

Area and perimeter of a rectangle can be defined using its length and breadth; the formula for area of a rectangle:

A = L x B

Perimeter of a rectangle can be calculated using the formula;

P = 2(L + B)

Volume of a rectangle can be easily calculated using length, breadth and height, the formula is;

V = L x B x H

Solid Shapes (3 Dimensional):

Solid figures are 3-dimensional figures that have length, width, and height. Few of the 3 D figures are listed below.

Volume

Volume of a cylinder:

Volume of a cylinder can be calculated by using radius and height of a cylinder. These can be used in following formula $\pi$ r2 h to get a volume.

Volume of a cylinder = $\pi r^2 h$

Volume of pyramids:

Volume of a pyramid can be calculated using a formula

Volume of a pyramid = $\frac{1}{3}$ BH

(B = base of a pyramid and H = height of a pyramid)

Volume of a cone:

Volume of a cone can be calculated using the following formula

Volume of a cone = $\frac{1}{3} \pi$ r2 h

Points On A Grid:

In geometry, a point on grid is used for 3D volume where the base cell has 6 faces (hexahedron). A set of straight lines defined by their end points define the pillars of the corner-point grid. A corner-point cell will gives out the volume between 4 neighboring pillars and two neighboring points on each pillar. Each cell can be denoted as (i,j,k), where the k coordinate runs along the pillars, and i and j span each layer.