Area Calculator

Purpose

In construction, the term "area" typically refers to a two-dimensional measurement of land, surface, or a specific part of a region.

The measurement of area is used to determine the necessary amount of material required to complete a task. In order to determine the amount of material required to cover a surface and labour cost for the particular task, such as a flooring, plastering, tiling, painting etc, it is necessary to calculate its surface area.

We all have learnt the formula to calculate area at school level. However, if anyone want to recall the formula, shape properties etc, may go further.

Shape covered in this calculator

1. Square
2. Rectangle
3. Triangle (3 Sides)
4. Triangle (Side, Angle, Side)
5. Triangle (Angle, Side, Angle)
6. Circle
7. Semi-Circle
8. Sector
9. Trapezoid
10. Parallelogram
11. Rhombus (Side, Height)
12. Rhombus (Diagonals)
13. Rhombus (Side, Angle)
14. Kite
15. Annulus (Ring)
16. Regular Polygon

Shape, Properties and Formula

1. Square
A square is a two-dimensional geometric shape that has four equal sides and four angles that are all equal to 90 degrees.

Properties

• Have four vertices and four sides of equal length.
• Each of the four interior angles is right angle, which measures 90 degrees.
• Each of the four sides of the square is congruent to one another.
• The sides of the square are parallel to one another and are opposite in direction.
• The diagonals of a square intersect at a 90-degree angle and bisect each other.
• The equality of the two diagonals of a square is a geometric property inherent to this particular type of quadrilateral.
• The square's diagonal bisects it into two congruent isosceles triangles.
• It can be observed that the length of the diagonals of a square exceeds that of its sides.
2. Rectangle
A square is a two-dimensional geometric shape that has four equal sides and four angles that are all equal to 90 degrees. A rectangle is a quadrilateral with parallel sides of equal length and four vertices each measuring 90 degrees is classified as a rectangle.

Properties

• It has four sides and four vertices.
• Each vertex exhibits an angle that is equivalent to 90 degrees.
• the pairs of opposite sides are congruent and parallel to each other.
• The diagonals intersect at their midpoint.
• The total of all internal angles of a rectangle is equivalent to 360 degrees.
3. Triangle
A triangle is a form of polygon with three sides. The vertex of a triangle is where two of its sides meet.

Properties

• In a triangle, the sum of the internal angles is always 180 degrees.
• The sum of the exterior angles of a triangle is always 360 degrees.
• The sum of consecutive interior and exterior angle is supplementary.
• The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is always greater than or equal to the length of the third side.
• The absolute value of the difference between the lengths of any two sides of a triangle is always less than the length of the third side.
• It is a well-established principle in geometry that the smallest interior angle of a triangle is always opposite the shortest side. Similar to that, the maximum interior angle is always positioned opposite to the longest side.
4. Circle
A circle is a set of points in a plane that are equidistant from a specific point known as the "center."

Properties

• The circumference of a circle is equidistant from its center.
• The circle's diameter bisects it into two identical sections.
• Circles possessing identical radii exhibit congruence with one another.
• The circle's diameter, which is the longest chord, measures twice the length of its radius.
5. Semi-Circle
The shape of a semicircle is created by cutting a circle in half or by dividing its circumference by two.
6. Sector
A sector is the portion of a circle that is enclosed by an arc and two radii. A sector divides the circle into two parts, namely Major and Minor Sector. The smaller area is known as the Minor Sector, whereas the larger area is known as Major Sector.
7. Trapezoid
A quadrilaterals that have two parallel sides and two non-parallel sides are known as Trapezoid.

Properties

• An isosceles trapezoid has equal diagonals and base angles.
• A trapezoid's median is parallel to the bases and equal to the average base length.
• The intersection point of the diagonals is collinear to the midpoints of the two opposite sides.
8. Rhombus
A rhombus is a special case of a parallelogram in which opposite sides are parallel and the opposite angles are equal. Moreover, all the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles.
9. Kite
A kite is a quadrilateral possessing two pairs of sides that are of equal length and are adjacent to each other.

Properties

• When the two sides that are not the same meet, they form a right angle.
• It can be seen as two triangles that are the same shape and have the same base.
• Its diagonals intersect each other at right angles.
• The longer diagonal bisect the shorter diagonal.
• The shorter diagonal divides the kite into 2 isosceles triangles.