A quadrilateral is a four-sided polygon (polygon with four sides, four angles, and four vertices).
In a quadrilateral, the sum of all the angles equals 360º degrees.
A Square is a quadrilateral with four right angles and all four sides of equal length.
A Rectangle is a quadrilateral with adjacent sides perpendicular (all four angles are therefore right angles). The opposite sides are parallel, and of equal length.
A Parallelogram is a quadrilateral whose opposite sides are parallel. The opposite sides are parallel, and of equal length. The opposite angles are equal. Consecutive angles are supplementary. The diagonals bisect each other in the center of the parallelogram.
A Rhombus (or equilateral quadrilateral) is a parallelogram with all sides equal, the opposite angles of a rhombus are congruent. The diagonals of a rhombus bisect each other. A rhombus with right angles is a square. The opposite sides are parallel. Consecutive angles are supplementary.
A Trapezoid is a polygon with four sides, two of which (the bases) are parallel to each other. The non-parallel sides are called the legs of the trapezoid.
An isosceles trapezoid is a trapezoid with congruent legs. The base angles (the angles on either side of the bases) are congruent.
A Kite is a quadrilateral with two pairs of sides next to each other that have equal length. But none of the sides are parallel.
Area of quadrilaterals
Area of a square = side²
Area of a rectangle = base ✕ height
Area of a parallelogram = base ✕ height
(The height of a parallelogram is the perpendicular distance between any pair of parallel sides)
A rhombus is a special case of a parallelogram with all sides being equal. So, area of a rhombus= base ✕ height
Area of a trapezoid = Average width × height
We can split the kite in half (using one of the diagonals) to create a pair of congruent triangles.
GE02 Square Area and Perimeter with Integers
GE01 Square Area and Perimeter with Decimals
GE03 Square Area and Perimeter with Decimals
GE06 Square Area and Perimeter with Decimals
GE04 Rectangle Area and Perimeter with Integers
GE05 Rectangle Area and Perimeter with Integers
GE07 Length and width of a rectangle given area
GE08 Length and width of a rectangle given perimeter
GE09 Rhombus Area (Decimals) 1
GE10 Rhombus Area (Decimals) 2
GE11 Rhombus Area (Decimals) 3
GE12 Area of a Kite
GE15 Area of a Trapezoid (integers)
GE13 Area of a Trapezoid (with decimals) 1
GE14 Area of a Trapezoid (with decimals) 2
Quadrilateral Classification: (regarding its interior angles)
Convex quadrilateral: all interior angles are less than 180°
Concave quadrilateral: one interior angle is bigger than 180°
AN19 Internal Angles
The sum of the interior angles of any quadrilateral is 360°