What is a square? Definition, formulas and exercises

A square is a figure with four equal sides. A square has four angles of 90 degrees (ninety degrees). As squares are closed figures, in geometry they are called polygons, and classified as quadrilaterals, figures with four sides.

Every square has four edges (sides), four vertices (where the sides meet) and four 90° interior angles.

Square

Where, l are the sides and: A, B, C and D the vertices.

Not every quadrilateral is a square. To be square, it must have four sides of the same measure, and four interior angles with 90º. The parallelogram and trapezoid are quadrilaterals, but not squares.

Squares are a category of two types of quadrilaterals: rectangles and rhombuses.

Every square is a rectangle. The definition of a rectangle is: a quadrilateral with two pairs of parallel sides, and the interior angles of 90º.

If the sides of the rectangle are equal in length, in this particular case, the rectangle will also be a square.

So while every square is a rectangle, not every rectangle is a square.

rhombus and square
A square is a rectangle with sides of the same length.
instagram story viewer

Every square is a rhombus. A rhombus is a quadrilateral with four sides of equal length. In the particular case where the rhombus has the four right angles, it is also a square.

rhombus and square
A square is a rhombus with four right angles.

perimeter of the square

The perimeter is the sum of the sides. Since a square has equal sides, the perimeter is:

straight P equals straight L straightest L straightest L straightest L equals 4 straight L

Where L, is the measure of the side.

square area

The area of ​​the square is the measure of its inner surface. It is calculated as the multiplication between two sides.

straight A equals straight L space. straight space L equals straight L squared

square diagonals

A diagonal is a line segment connecting two vertices not on the same sides. In this case, a square has two diagonals.

square diagonals

A diagonal divides the square into two isosceles right triangles. In this case, the measure of the diagonal of the square is also the measure of the hypotenuse of a right triangle with equal legs.

Where L is the measure of the sides of the square, applying the Pythagorean Theorem, the diagonal is calculated by:

straight D equals square root of straight L squared plus straight L squared end of root straight D equals root square of 2 straight L squared end of root bold D bold equals bold L square root of bold 2

Exercises on square

Exercises 1

Find the perimeter of a square with side 14 cm.

P = 14 + 14 + 14 + 14 = 56 cm

Exercise 2

Find the area of ​​a square with sides of 9 cm.

straight A equals straight L space. straight space L space equals straight space L squared square A equals 9 squared space equals space 81 space cm squared

Exercise 3

Find the length of the diagonal of a square with sides of 5 cm.

D equals square root of 5 squared plus 5 squared end of root D equals square root of 25 space plus space 25 end of root D equals square root of 50

Factoring the 50:

Factorization of 50.

The 50 can be written as:

D equals the square root of 2 space. space 5 squared end of root D equals square root of 2 space. space square root of 5 squared end of root D equals 5 square root of 2

The diagonal measures 5 square root of 2 cm.

See more about:

  • quadrilaterals
  • Square perimeter
  • Square Area
  • Area and Perimeter
  • polygons

  • quadrilaterals
  • polygons
  • Rectangle
  • Areas of Plane Figures
  • Square Area
  • Plane Geometry
  • parallelogram
  • Polygon Area
Teachs.ru
Pythagorean Theorem: formula and exercises

Pythagorean Theorem: formula and exercises

O Pythagorean theorem lists the length of the sides of the right triangle. This geometric figure ...

read more
Cartesian Plan Definition and Exercises

Cartesian Plan Definition and Exercises

Cartesian plan is a method created by the French philosopher and mathematician, René Descartes. T...

read more
Cylinder Area Calculation: formulas and exercises

Cylinder Area Calculation: formulas and exercises

THE cylinder area corresponds to the surface measurement of this figure.Remember that the cylinde...

read more
instagram viewer