Triangle

Three sides connected to each other resulting a closed contour is known as triangle. As shown in the figure below, it’s edges and angles are represented in this format: Angles are represented with capital letter A, B and C (or sometimes written as ∠BAC, ∠ABC and ∠ACB) and the edge opposite to angles A, B and C are named as a, b and c respectively.

Properties:

• It has three angles each at the joining of two sides
• All three angles of a triangle sum to 180
• The ratio of side length to the sine of its opposite angle is the same for all three sides. Mathematically, it can be expressed as
  • \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
• Perimeter of triangle, 2s = a + b + c
• Area of triangle if height is given = \frac{1}{2} \times \text{base}(a) \times \text{height}(h)
• Area of triangle = \sqrt{s(s-a)(s-b)(s-c)} Where s is the half of its perimeter

Parallelogram:

A parallelogram is a four sided shape which is described by following properties:

Properties:

• Opposite sides are parallel to each other
• Opposite sides are equal in length
• Diagonals of parallelogram bisects each other
• Sum of all interior angles are equal to 360^o
• None of the angles equal to 90^o
• Opposite angles are equal
• Perimeter  = 2(AB+AD)
• Area = \text{base} \times \text{height} = AB\times h

Rhombus

A rhombus is a four sided shape which is described by following properties

Properties:

• Opposite sides are parallel to each other
• All sides are equal in length
• Diagonals of rhombus are perpendicular bisector
• Sum of all interior angles are equal to 360^o
• None of the angles equal to 90^o
• Opposite angles are equal
• Perimeter  = 4a (where a is the length of a side)
• Area = \frac{1}{2} \times \text{diagonal element1} \times \text{diagonal element2}

Rectangle

A rectangle is a four sided shape with the following properties

Properties:

• Opposite sides are parallel to each other
• Opposite sides are equal in length
• Diagonals of rectangles are equal and bisects each other
• Sum of all interior angle are equal to 360^o
• Each of the interior angle is equal to 90^o
• Perimeter = 2×(AB+AD)
• Area = AB×AD

Square

A square is a four sided shape with the following properties

• Opposite sides are parallel to each other

• Diagonals of squares are equal
• Diagonals of squares are perpendicular bisector
• All sides are equal in length
• Sum of all interior angle are equal to 360^o
• Each of the interior angle is equal to 90^o
• Perimeter = 4×AB
• Area = AB²

Circle

A circle is defined by its center, c and radius, r such that distance of any point on circle from its center is always equal to its radius. Circle has the following properties

• Diameter is defined as the line drawn from any point on circle, passes through the center, ends at other point on circle. Diameter, d = AB = 2r
• Perimeter = 2πr
• Area = πr²
• Any triangle drawn on semicircle is always a right triangle. Triangle ACB is right triangle.
• Any segment of circle is known as arc
• Angle created by an arc at the center is twice as the angle created by the same arc on the circumference. \angle DOF = 2 \angle DEF

Trapezoid

A trapezoid is a four sided shape with only one pair of sides are parallel. It has the following properties:

• Two sides are parallel and other two sides are nonparallel
• Opposite angles are supplementary and sum of opposite side angles are 180^o
• Perimeter = AB + BC + CD + AD
• Area = \frac{1}{2} \times \text{sum of parallel sides} \times \text{height} = \frac{1}{2}(a+b)h

Polygon

A polygon is a general term which is defined by the number of sides it encompasses. For example, a three side polygon is known as triangle, a five side polygon is known as pentagon.

Properties

• Number of diagonals of a polygon  = \frac{n(n-3)}{2}  where n is the number of vertices in the polygon
• Sum of interior angles of polygon  =   (n-2)\times 180^\circ where n is the number of sides.