From the latin root: quadri - four; latus - sideDefinition: a closed four-sided figure. All of its sides must be straight. There are many different kinds of quadrilaterals, but all of them have several things in common. They all have four sides and four vertices, and their interior angles all add up to 360 degrees. We know many quadrilaterals by their special shapes and properties, like squares. Remember, if you see the word quadrilateral, it does not necessarily mean a figure with special properties like a square or rectangle! In word problems, be careful not to think that a quadrilateral has parallel sides or equal sides unless that is stated.

Regular Quadrilaterals:

Rectangle

A rectangle is a quadrilateral with all of its interior angles equal to 90°. The opposite sides of a rectangle run parallel to each other. A rectangle can also go under the parallelogram catergory. A square is a type of rectangle.

Area of a Rectangle Formula:
A=lw

Example:

a=3cm
b=5cm

A=lw =5x3
=15cm²

Therefore, the area of the rectangle is 15cm².

Perimeter of a Rectangle
Formula;
P=2(l+w)

Example:

a=3cm
b=5cm

P=2(l+w)
=2(3+5)
=2(8)
=16cm

Therefore, the perimeter of the rectangle is 16cm.

Squares

A square is a quadrilateral with all four of it's sides and angles equal. All of it's interior angles are 90°. Another quality of a square is that if you were to draw lines connecting opposet vertexes (corners) the diagonals would intercept at a 90° angle (or perpendicular). A square can be considered as a rectangle, parallelogram, or rhombus.

Area of a Square:

Formula:
A=s²

Example:

a=10cm

A=s²
=10²
=100cm²

Therefore, the area is 100cm².

Perimeter of a square:

Formula:
P=4s

Example:

a=10cm

P=4s
=4x10
=40cm

Therefore, the perimeter is 40cm.

Parallelograms

Parallelogram

Opposite sides of a parallelogram are parallel and equal in length. The opposite angles are congruent. Angles "a" are the same, and angles "b" are the same. Squares, Rectangles and Rhombuses are all Parallelograms.

Any side of a parallelogram can be the base. Once you have the base, the height of the parallelogram is the length of any line segment perpendicular from the base parallel to the opposite side. Also, adjacent angels of a parallelogram always have a sum of 180 degrees. Each diagonal bisects one another.

The area of a parallelogram is A = b x h, "b" representing the length and "h" representing the height.
Example:
A=?
b=10cm
h=5cm
A = b x h
A = 10 x 5
A = 50cm² The area is 50 cm².

The perimeter of a parallelogram is the distance around the outside of it. The formula is side + side + side + side, since a parallelogram has four sides. With opposite sides being congruent, you could use the formula 2s+2s as long as you used two different sidelengths.
Example:

P = S+S+S+S
P = 8 cm + 8cm + 3 cm + 3 cm = 22 cm
Therefore, the perimeter is 22cm.

Rhombus A rhombus is a different type of parallelogram. Instead of having opposite sides parallel and equal in length, all the sides of a rhombus have equal length. A rhombus has some of the same characteristics of a square but not all angles need to be 90°. All sides of a rhombus and be named the base because they are all equal.

Area of a rhombus: A=ba

A= base × altitude (altitude is also known as height)

Trapezoids A trapezoid is a quadrilateral with one pair of parallel sides. The pair of parallel sides are not the same length, but the other two sides are. A trapezoid also has two obtuse angles, and two acute angles. Area of a Trapezoid: Formula:
A= h[(b1+b2)/2]

Therefore, the perimeter of the trapezoid is 29cm.

Quadrilaterals - How Do They Relate To The Real World?

Many of our everyday items are quadrilaterals. Example. paper - rectangle, kite - rhombus, piece of cheese - square. :P Quadrilaterals are all around us so we need to know about them!

Why Do We Need To Know The Perimeter of Quadrilaterals?

There are some problems that we may come across, in which case we need to know how to solve them by learning about the perimeter of quadrilaterals.

Example:

Harley lives in a house with a square yard around it. Each side of her yard is 20m. She wants to build a fence around it, and her house (which is inside it). How much fencing will she need?

-->To figure this out, we need to know the perimeter of her yard because that will tell us how much fencing she needs. To find the perimeter we need to know how to figure it out! Because we know the perimeter, this is how we find the answer:

P=4s
=4x20m
=80m

Therefore, Harley needs 80m of fencing because the perimeter of her backyard is 80m.

Why Do We Need To Know The Area Of Quadrilaterals?

In real life, there are lots of problems, and jobs, that deal with area. So, to figure them out, we need to know how!

Example:

Harley's house has a rectangular bathroom. The dimensions of her bathroom is 3m by 4m. Harley wants to cover the whole bathroom floor with tiles. How much tiles does she need?

-->To figure this out, we need to know the area of Harley's bathroom, because that will tell us how much tiling she will need to cover it. So, we use our area formula for a rectangle to get the answer:

A=lxw
=3x4
=12m²

Therefore, Harley needs 12m² of tiling to cover her whole bathroom floor.

Irregular Quadrilaterals:
Irregular quadrilaterals still have four sides and four angles. Here are the differences between a regular and irregular quadrilateral:

REGULAR QUADRILATERALS IRREGULAR QUADRILATERALS- all four of its angles are convex (less than 180°) -can have concave angles (more than 180°) -have at least pme set of parallel sides - do not have any parallel sides-can have some or all of their side lengths the same - all of their side lengths can be different

Here is an example of an irregular quadrilateral:

It is an irregular concave square. This is BECAUSE... - it has a concave angle
- it has no parallel sides

EVEN THOUGH SOME OF ITS SIDE LENGTHS ARE EQUAL, IT IS STILL IRREGULAR BECAUSE OF ITS OTHER ATTRIBUTES

Some Other Pages That Might Help Your Understanding:

MARKED

From the latin root:Quadrilateralsquadri- four;latus- side Definition: a closed four-sided figure. All of its sides must be straight.There are many different kinds of quadrilaterals, but all of them have several things in common. They all have four sides and four vertices, and their interior angles all add up to 360 degrees. We know many quadrilaterals by their special shapes and properties, like squares. Remember, if you see the word quadrilateral, it does not necessarily mean a figure with special properties like a square or rectangle! In word problems, be careful not to think that a quadrilateral has parallel sides or equal sides unless that is stated.

## Regular Quadrilaterals:

Rectangle## A rectangle is a quadrilateral with all of its interior angles equal to 90°. The opposite sides of a rectangle run parallel to each other. A rectangle can also go under the parallelogram catergory. A square is a type of rectangle.

Area of a Rectangle

Formula:

A=lw

Example:

a=3cm

b=5cm

A=lw

=5x3

=15cm²

Therefore, the area of the rectangle is 15cm².

Perimeter of a Rectangle

Formula;

P=2(l+w)

Example:

a=3cm

b=5cm

P=2(l+w)

=2(3+5)

=2(8)

=16cm

Therefore, the perimeter of the rectangle is 16cm.

A square is a quadrilateral with all four of it's sides and angles equal. All of it's interior angles are 90°. Another quality of a square is that if you were to draw lines connecting opposet vertexes (corners) the diagonals would intercept at a 90° angle (or perpendicular). A square can be considered as a rectangle, parallelogram, or rhombus.SquaresArea of a Square:Formula:

A=s²

Example:

a=10cm

A=s²

=10²

=100cm²

Therefore, the area is 100cm².

Perimeter of a square:Formula:

P=4s

Example:

a=10cm

P=4s

=4x10

=40cm

Therefore, the perimeter is 40cm.

ParallelogramsAny side of a parallelogram can be the base. Once you have the base, the height of the parallelogram is the length of any line segment perpendicular from the base parallel to the opposite side. Also, adjacent angels of a parallelogram always have a sum of 180 degrees. Each diagonal bisects one another.

The area of a parallelogram is A = b x h, "b" representing the length and "h" representing the height.

Example:

A=?

b=10cm

h=5cm

A = b x h

A = 10 x 5

A = 50cm²

The area is 50 cm²

.The perimeter of a parallelogram is the distance around the outside of it. The formula is side + side + side + side, since a parallelogram has four sides. With opposite sides being congruent, you could use the formula 2s+2s as long as you used two different sidelengths.

Example:

P = S+S+S+S

P = 8 cm + 8cm + 3 cm + 3 cm = 22 cm

Therefore, the perimeter is 22cm.

RhombusA rhombus is a different type of parallelogram. Instead of having opposite sides parallel and equal in length, all the sides of a rhombus have equal length. A rhombus has some of the same characteristics of a square but not all angles need to be 90°. All sides of a rhombus and be named the base because they are all equal.

Area of a rhombus:A=ba

A= base × altitude (altitude is also known as height)

TrapezoidsA trapezoid is a quadrilateral with one pair of parallel sides. The pair of parallel sides are not the same length, but the other two sides are. A trapezoid also has two obtuse angles, and two acute angles.

Area of a Trapezoid:Formula:

A= h[(b1+b2)/2]

Example:

a= 10cm

b=9cm

c=5cm

height: 4cm

A= h[(b1+b2)/2]

= 4[(10+9)/2]

= 4(19/2)

= 4x19.5

= 38cm²

Therefore, the area of this trapeziod is 38cm².

Perimeter of a Trapezoid:Formula:

P= s+s+s+s

Example:

a= 10cm

b=9cm

c=5cm

P=s+s+s+s

=10+9+5+5

=29cm

Therefore, the perimeter of the trapezoid is 29cm.

Quadrilaterals - How Do They Relate To The Real World?Many of our everyday items are quadrilaterals. Example. paper - rectangle, kite - rhombus, piece of cheese - square. :P Quadrilaterals are all around us so we need to know about them!

Why Do We Need To Know The Perimeter of Quadrilaterals?

There are some problems that we may come across, in which case we need to know how to solve them by learning about the perimeter of quadrilaterals.

Example:

Harley lives in a house with a square yard around it. Each side of her yard is 20m. She wants to build a fence around it, and her house (which is inside it). How much fencing will she need?

-->To figure this out, we need to know the perimeter of her yard because that will tell us how much fencing she needs. To find the perimeter we need to know how to figure it out! Because we know the perimeter, this is how we find the answer:

P=4s

=4x20m

=80m

Therefore, Harley needs 80m of fencing because the perimeter of her backyard is 80m.

Why Do We Need To Know The Area Of Quadrilaterals?In real life, there are lots of problems, and jobs, that deal with area. So, to figure them out, we need to know how!

Example:

Harley's house has a rectangular bathroom. The dimensions of her bathroom is 3m by 4m. Harley wants to cover the whole bathroom floor with tiles. How much tiles does she need?

-->To figure this out, we need to know the area of Harley's bathroom, because that will tell us how much tiling she will need to cover it. So, we use our area formula for a rectangle to get the answer:

A=lxw

=3x4

=12m²

Therefore, Harley needs 12m² of tiling to cover her whole bathroom floor.

Irregular Quadrilaterals:

Irregular quadrilaterals still have four sides and four angles. Here are the differences between a regular and irregular quadrilateral:

REGULAR QUADRILATERALS

IRREGULAR QUADRILATERALS- all four of its angles are convex (less than 180°)

-can have concave angles (more than 180°) -have at least pme set of parallel sides

- do not have any parallel sides-can have some or all of their side lengths the same

- all of their side lengths can be different

Here is an example of an irregular quadrilateral:

It is an irregular concave square. This is BECAUSE...

- it has a concave angle

- it has no parallel sides

Some Other Pages That Might Help Your Understanding:Angles

Composite FiguresGeometryOptimal ValuesParallel and Perpendicular LinesPolygons

Citations**Page, John (2007) Rhombus. Math Open Reference 2007. Retrieved December 13, 2008 from: http://www.mathopenref.com/rhombus.html

Pierce, R. (n.d.).

Quadrilaterals. Retrieved November 17, 2008, from http://www.mathsisfun.com/quadrilaterals.htmlSanchez, P. (2007, July 18).

Parallelograms. Retrieved December 16, 2008, from http://planetmath.org/encyclopedia/Parallelogram.htmlPage, John. (2007)

Trapezoid.Math Open Reference 2007. Retrieved December 17, 2008 from: **http://www.mathopenref.com/trapezoid.html**Page, John. (2007)

Square. Math Open Reference 2007. Retrieved December 17, 2008 from: http://www.mathopenref.com/square.htmlWeisstein, Eric W.(1999-2008)

Square. Wolfram MathWorld. Retrieved December 17, 2008 from: http://mathworld.wolfram.com/Square.htmlPage. John. (2007).

Quadrilaterals. Math Open Reference 2007. Retrieved December 18, 2008 from: http://www.mathopenref.com/quadrilateral.htmlPage, John. (2007).

Irregular Polygons. Math Open Reference 2007. Retrieved December 18, 2008 from: http://www.mathopenref.com/polygonirregular.htmlPage, John. (2007).

Perimeter of a Rectangle. Math Open Reference 2007. Retrieved December 18, 2008 from: http://www.mathopenref.com/rectangleperimeter.htmlPage, John. (2007). Rectangle. Math Open Reference 2007. Retrieved December 18, 2008 from: http://www.mathopenref.com/rectangle.html

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