Surface of usual surfaces

of usual express yourself using simple formulas. One can estimate the surface of a surface with the contours complicated by summoning simpler surfaces of surfaces. This point of view leads to the calculation of .

Synopsis 1 Surface of plane surfaces 1.1 Square 1.2 Rectangle 1.3 Triangle 1.4 Trapezoid 1.5 Rhombus 1.6 Parallelogram 1.7 Disc and ellipse 2 Surface in dimension 3 2.1 Cubic 2.2 Parallelepiped 2.3 Sphere 2.4 Cap or spherical zone

Surface of plane surfaces

Square

The surface of the square is calculated while multiplying on the side by itself. If the side is named has, the surface With is thus worth

With = has².

From where it of the expression square of a number.

Rectangle

If the lengths on the sides are <maths>a</maths> and <maths>b</maths>, then the surface of is worth the product

With = has × B.

Triangle

If ABC is one (unspecified), is H the height of the triangle out of B (the length of segment [ BH ], H the being projected orthogonal one of B on (AC)) and B is the length of the segment [ AC ], then the surface of the triangle is worth

With = (B × H)/2.

See .

See also: Formulate of Héron.

Trapezoid

The surface of is worth the product its height by the half the sum of its bases.

Rhombus

If has and B are the lengths of its diagonals, then the surface of is

With = (has × B)/2

See .

Parallelogram

For one whose adjacent sides have as lengths has and B and form an angle?, the surface is worth

With = has × B × sin(?)

Disc and ellipse

The surface of one of ray R is worth

With =? × R²

This formula spreads inside one of which has and B are the semi-axes:

With =? × has × B

Surface in dimension 3

Cubic

The surface of cubic of edge has is worth

With = 6 × has²

they are indeed six squares on side has.

Parallelepiped

The surface of parallelepiped rectangle on sides has, B and C is worth

With = 2 × (ab + bc + Ca);

indeed, its faces are rectangles. If the parallelepiped is not right-angled, the faces are parallelograms, one thus moderates each product by a sine (cf supra: parallelogram).

Sphere

The surface of one of ray R is worth

With = 4 ×? × R²

Cap or spherical zone

The surface of a cap or a spherical zone height H located on a sphere of ray R is worth

With = 2 ×? × R × H

This is shown by assimilating bands height infinitesimal dh with plane bands, and while integrating on dh.