Calculate area, perimeter, diagonal, and radii of a square from side length
Area:
A = s²
where s is the side length
Perimeter:
P = 4s
where s is the side length
Diagonal:
d = s√2
approximately 1.414 times the side length
Circumradius (radius of circumscribed circle):
R = d/2 = s√2/2
radius of circle passing through all vertices
Inradius (radius of inscribed circle):
r = s/2
radius of circle touching all sides
A square is a special quadrilateral with all four sides equal in length and all four angles equal to 90 degrees. It's both a rectangle (with equal sides) and a rhombus (with right angles), making it the most regular quadrilateral.
The diagonal of a square can be calculated using the Pythagorean theorem. Since a diagonal divides a square into two right triangles, d = s√2, where s is the side length. This equals approximately 1.414 times the side length.
The circumradius is the radius of the circle that passes through all vertices of the square (circumscribed circle). The inradius is the radius of the circle that touches all sides of the square from inside (inscribed circle). For a square, the circumradius is √2 times the inradius.
Square calculations are essential in construction (room dimensions, tiles), land measurement, graphic design, computer screens and displays, game boards, city planning, and countless other applications. The square is one of the most fundamental shapes in engineering and design.
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