Finding the Area of a Basic Figure Developing the Area formulae for Squares, Rectangles, Parallelograms, Triangles, and Trapezoids. Squar e Parallelo gram Trian gle Rectang le Trapezoi d
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Finding the Area of a Basic Figure
Developing the Area formulae for Squares, Rectangles, Parallelograms, Triangles, and
Trapezoids.
Square Parallelogram Triangle
Rectangle Trapezoid
What is Area?
Area is a quantity that describes the amount a two-dimensional shape can cover a plane.
Area is defined as the number of squares of a fixed size that cover the same space.
Area can be thought of as the amount of material it can take to cover an object OR the amount of paint required to paint an object with a single coat
What is Area?Since Area is measured in Square units we will start by defining the area of a unit square.
1 unit
1 unit
The Area of this object is Defined as 1 unit2.
The Area of a Square
To find the area of a square we find how many unit squares fit into the actual square
4 units
4 units
The Area of this object is 16 units2.
The Area of a Square
Following the pattern for any Square we can develop a formula
S units
S units
The Area of this object is S*S units2
or S2 units2
The Area of a Square
SO….The Area of any square is:
Area = S2
(Where S is the length of the sides of the Square)
S units
S units
The Area of a Rectangle
We find the area of a rectangle similarly to how we found the area of a rectangle.
3 units
6 units
The Area of this object is 6*3 = 18 units2.
The Area of a Rectangle
Now we develop the formula by multiplying the number of columns (Base) with the number of rows (Height).
Height
Base
The Area of this object is Base*Height = bh units2.
The Area of a Rectangle
SO….The Area of any rectangle is:
Area = b*h(Where b is the base and h is the height)
Height
Base
The Area of a Parallelogram
To Find the Area Formula for Parallelograms we must slice it and turn it into a Rectangle
Height
Base
The Area of a Parallelogram
Start by identifying a line of height perpendicular to the base.
Height
Base
The Area of a Parallelogram
Cut the Parallelogram along the height and move half the shape to the other side.
Height
Base
Base
Height
The Area of a Parallelogram
Notice that the shape turned into a Parallelogram with the same Height and Base
Height
Base
Base
Height
The Area of a Parallelogram
SO…the are formula for a Parallelogram IS identical to the Area formula for a Rectangle.
Height
Base
Base
HeightArea = b*h
Where b is the base
and h is the height
Parallelogram Example
8
10
Area = b*h = 10*8 = 80 units2
The Area of a Triangle
Again the goal is to turn the triangle into a shape we already know
Height
Base
The Area of a Triangle
Start by Copying the Triangle
Height
Base
The Area of a Triangle
Rotate the copy and place it next to the original so that one pair of common sides overlap
Height
Base
Notice: The new shape is a Parallelogram & the triangle was half of the new shape.
The Area of a Triangle
Since the original triangle is half of the Parallelogram, then the area is also half.
Height
Base
Area = (Area of Parallelogram) = b*h
Triangle Example
4
6
Area = = *4 = 12 units2
The Area of a Trapezoid
Again the goal is to turn the trapezoid into a shape we already know
Height
Base 2
Base 1
The Area of a Trapezoid
Like the triangle, copy the original trapezoid
Height
Base
The Area of a Trapezoid
Rotate the trapezoid and place it so one pair of legs overlap
Height
Base 2Notice: The new shape is a Parallelogram & the trapezoid was half of the new shape.
Base 1
Base 1Base 2
The Area of a Trapezoid
Since the Trapezoid is half the parallelogram:
Height
Base 2
Area = b*h =
*h
Base 1
Base 1Base 2
Trapezoid Example
4
8Area = *h
= *4=(13)*4
= 6.5*4
= 26
5
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