Quadrilaterals

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.

 

 

 

 

 

 

 

 

 

 

Quadrilateral Family

 

 

 

 

 

 

 

 

 

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

 

 

 

 

 

Area of a Kite.  The area of a kite is half the product of the diagonals.

We can split the kite in half (using one of the diagonals) to create a pair of congruent triangles.

 

 

Quadrilaterals

Area of a Square

Area of a Rectangle

Area of Parallelograms

Area of a Trapezoids

Parallelogram

Perimeter of a Rectangle

Perimeter of a Square

 

 

 

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

 

AR10   Area of a parallelogram 1

AR11   Area of a parallelogram 2

AR12   Finding the base or height of a parallelogram.

Quadrilateral Classification: (regarding its interior angles)

Convex quadrilateral: all interior angles are less than 180°

Concave quadrilateral: one interior angle is bigger than 180°

 

 

 

 

AN20  Missing Angle in quadrilaterals