Equilateral Square

Equilateral square is a geometry figure, square has four sides all the four sides are equal in length then it is said to be equilateral square. In two dimensions square we find only the area. The area is measured in terms of square units. In three dimensions, square is called cube it is also equilateral for that we find the volume only the figure has length, width and height.

Formula for equilateral square:

Area Formulas for equilateral square

The area of a square can be found by multiply the base times itself

Area of square = side × side or a2

Volume of cube =side x side x side a3



AB = BC = CD = AD

Then it is Equilateral Square

Problem for area of square:

1) Find the area of the square, length of one side id 9cm

Solution:

Given: Side a = 9cm

Area of square = a2

= 9 × 9

Area of square = 81cm2

Problems for volume of square

2) Find the volume of the cube its side is 9cm

Solution:

Given: side =9cm

Volume of cube = a3

= a × a × a

= 9 × 9 × 9

= 729cm3

3) Find the area of the square, length of one side id 4m

Solution:

Given: Side a = 4m

Area of square = a2

= 4 × 4

Area of square = 16m2

Problems for volume of square

4) Find the volume of the cube its side is 12m

Solution:

Given: side = 12m

Volume of cube = a3

= a × a × a

= 12 × 12 × 12

= 1728 m3

Examples for equilateral square:

Prove by distance formula that the square is a equilateral square:



Formula  = √(x2 - x1)2+(y2 - y1)2

A(0,0) B(0,1) C(1,1) D(1,0)

Length of AB = √(x2 - x1)2+(y2 - y1)2

AB = √(0-0)2 + (1-0)2

= √0+(1)2

= 1

Length of BC = √(x2 - x1)2+(y2 - y1)2

BC = √(1-0)2 + (1-1)2

= √(1) + (0)

= 1

Length of CD = √(x2 - x1)2+(y2 - y1)2

CD = √(1-1)2 + (0-1)2

= √(0) +(-1)

= 1

Length of AD = √(x2 - x1)2+(y2 - y1)2

AD =√ (1-0)2 + (0-0)2

= √(1) + 0

= 1

Therefore AB = BC = CD = AD =1

All the sides are equal then the square is equilateral square.