definition:


A square is a a regular polygon (flat shape) with four equal sides. 

  

area of a square:


a) The area is the side length squared.

formula:

example: 

problem: A square has a side length of 8 m. What is its area?

answer:

Area = a x a

Area = 8 m x 8 m 

Area = 64 m²

 

b) The area is also half of the diagonal squared:

formula:

example: 

problem: A square has a diagonal length of 12 m. What is its area?

answer:

Area = d * d/2  

Area = 12 m x 12 m : 2 

Area = 72 m² 

 

perimeter of a square


The perimeter is the distance around the edge and therefore 4 times the side length:

formula:

example: 

problem: A square has a side length of 6 cm. What is its perimeter?

answer:

Perimeter = 4 x a

Perimeter = 6 × 4 cm 

Perimeter = 24 cm

 

diagonals of a square:


The diagonal is the side length times the square root of 2: 

formula:

example: 

problem: A square has a side length of 3 m. What is the length of a diagonal?

answer:

Diagonal = a x √2

Diagonal = 3 x √2

Diagonal = 4,24 m  (to 2 decimals)

 

properties:


All sides of a square are equal in length/are congruent.

Every square has 4 vertices.

Each internal angle of the square is 90°.

The two diagonals are congruent and equal in length. 

The diagonals intersect in the middle.

The length of each side is the distance of two adjacent points (AB, BC, CD, AD).

The length of the diagonals ist the distance between opposite corner (AC, BD).

The perimeter is the distance around the square.

The Area is the side length squared.

 

problem 1  answer


Find the area and the perimeter of a square with each side measuring 2.9 centimeters.

 

problem 2  answer


The area of a square is 169 square meters.

a) length  of the square?

b) perimeter of the square?

 

problem 3  answer


The perimeter of a square is 68 inches.

a) length of the square?

b) area of the square?

 

problem 4   answer


The length of a square garden is 48 meters.

What will be the cost of grassing it, if you have to calculate $ 0.8 per square meters.

 

problem 5   answer


The length of a square is 28 feet.

a) Calculate the diagonal of the square.

b) Calculate the area of the square with the diagonal formula.

 

PDF-Worksheets


instructions   worksheet 1  worksheet 2  

 

more interesting articles: