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in mathematics, the circle designates exclusively the curved line, the surface being, as for it, called disc. The ratio of the circumference of the circle to its diameter defines the number pi. Other terms deserve to be defined: A chord is a line segment whose ends are on the circle; An arc is a portion of a circle delimited by two points; An arrow is the segment connecting the midpoints of an arc of a circle and a chord defined by two same points of the circle; A ray is a line segment joining the center to a point on the circle; A diameter is a rope passing through the center; it is a line segment that delimits the disk in two equal parts. The diameter is composed of two collinear rays; its length is 2r; A disc is a region of the plane bounded by a circle; A circular sector is a part of the disk between two radii; An angle in the center is an angle formed by two rays of the circle; The circumference is the perimeter of the circle and is equal to 2*pi*r.
The ellipse is one of the three conics (with the parabola, and the hyperbola whose circle can be considered as a particular case) discovered by Greek mathematicians as an intersection of a cone by a plane
The ellipse is a perspective circle: concretely, it is obtained by projecting obliquely the halo of a lampshade of a bedside lamp (lit preferably ...) on a wall. Independently of the conics, the ellipse can be thus defined (Apollonius) as a set of points.
A triangle is a polygon (closed planar figure bounded by several line segments) that has 3 sides, 3 vertices and 3 angles.
Any triangle: - 3 different sides - 3 unequal angles - The sum of the angles is equal to 180° .
Isosceles triangle: - 2 equal sides: AC = CB - 2 equal angles: CAB = CBA
Equilateral or regular triangle: - 3 equal sides - 3 equal angles (60°)
Rectangle triangle: This is half of a rectangle. - 1 right angle (90°) - The opposite side to the right angle is called the hypotenuse.
Isosceles triangle rectangle: - 1 right angle - 2 equal sides
A hexagon (from greek hexi = six and gonia = angle) is a polygon with six vertices and six sides. The internal angles of a regular hexagon are all 120 ° and its sides are of the same size. Regular hexagons can juxtapose each other without leaving any gaps, such as equilateral squares and triangles, and are thus useful for constructing tessellations. The cells of the rays in a hive of honey bees are hexagonal for this reason and because this form allows an efficient use of space and building materials.
A parallelogram is a quadrilateral whose sides are parallel two by two
- in a parallelogram, the opposite sides are equal
- in a parallelogram, the diagonals intersect in their middle
- in a parallelogram, the point of intersection of the diagonals is the center of symmetry. It's called the center of the parallelogram
- in a parallelogram, the opposite angles are equal, and the consecutive angles are additional.
- if a quadrilateral has opposite sides equal to two by two, then it is a parallelogram.
- if a quadrilateral with two sides both parallel and equal, then it is a parallelogram.
- if a quadrilateral has a center of symmetry, then it is a parallelogram.
- If a quadrilateral has diagonals that intersect in the middle, then it is a parallelogram.
A rectangle is a quadrilateral that has three right angles
A rectangle is a parallelogram. So he has all the properties of the parallelogram. The diagonals of a rectangle are equal. A rectangle has two axes of symmetry: the mediators of the sides.
Squares are geometric figures with 4 equal sides, 4 vertices and 4 right angles.
The diagonals of the square are the segments that connect the opposite vertices. They are the same length and intersect perpendicular to the center of the square.
To calculate the perimeter of a square, add the length of the 4 sides.
To calculate the area of a square, we multiply the lengths of 2 consecutive sides.
A convex quadrilateral is a rhombus if and only if one of the following propositions is satisfied:
Its four sides have the same length.
Its diagonals bisect internal angles.
Its diagonals are perpendicular and intersect in their middle.
Parallelogram of which two consecutive sides have the same length.
Parallelogram whose diagonals are perpendicular.
Parallelogram with a diagonal bisector of an internal angle.
A trapezoid is a quadrilateral with two parallel opposite sides. These two parallel sides are called bases. With this definition, the quadrilaterals ABCD and ABDC of the figure are both trapezoids (whose sides (AB) and (CD) are parallel). Some authors impose as an additional condition the convexity of the quadrilateral, which amounts to excluding "crossed trapezes" such as ABDC.