Transcript AREAS OF POLYGON

AREAS OF POLYGON
rectangle
Rectangular
region
The first figure above is a rectangle and
the second is a rectangular region.
rectangle
Rectangular
region
A rectangular region is a union of a
rectangle and its interior.
When you are asked to find the area of a
rectangle, you are actually asked to determine
the area of a rectangular region.
AREAS of a polygonal region
-
is the number of
square units contained
in the region.
A square unit is a square
with a side 1 unit in
length.

AREAS of a polygonal region
 A unit
for measuring area can
be any shape we choose. But
for convenience and by
tradition, we use a square
whose sides are a unit for
measuring length, and refer to
its area as one “ square unit”
1 unit
1 unit
The standard units of area are square units, such as
square centimeters, square decimeters and
square meters.
1
2
9
10
17
18
3
4
5
6
7
8
11
12
13
14
15
16
19
20
21
22
23
24
In the rectangle above, each small
The area can be determined by counting
square
is one
unitsquares.
in length.
the
number
of small
Since there
Find
of the
rectangle.
are
24 the
smallarea
squares,
therefore,
the area is
24 square units.
A= lw
where l is the
length and w
is the width.
w
l
l
w
8 units
3 units
The
area can be determined by counting
Solution:
the
of small squares. Since there
A =number
lw
are=24
small squares, therefore, the area is
8(3)
24
units.units
A square
= 24 square
A= (s)(s)
or
A = s²
Where s is the
length of a side.
s
s
Solution:
A = s²
=(5 cm)²
A= 25 cm²
5 cm
5 cm
h(height)
h
=w
=l
bb
(base)
In the figure, h is the height and b is the base.
Thus,
Area of a //gram = Area of a rectangle
= lw
By substitution,
A = bh
h = 4 cm
b = 6 cm
Solution:
Area of a //gram = bh
= (6 cm)(4 cm)
A = 24 cm²
h(height)
b (base)
In the figure, h is the height and b is the base.
Thus,
Area of a triangle = ½ Area of a parallelogram
A
= ½ bh
h= 8 cm
b = 10 cm
Solution:
= ½ bh
=½ (10 cm) (8 cm)
= ½ (80 cm²)
A = 40 cm²
A
What is a trapezoid?
- A quadrilateral
with one pair of
parallel sides.
In the figure, b1 & b2
are the bases and h
is the height .
Note:
Height (h) is a segment drawn from
a vertex of any polygon  to the
opposite side
.
b1
h
b2
b1
The formula to find the
area of a trapezoid was
derived from the area of
a triangle.
h
b2
Look at this…………..
Do
youdraw
knowa why
the
If you
diagonal,
height
ofare
thethe
triangles
what
new
are the
same?
figures formed?
b1
I
II
b2
Triangle
1 and 1Triangle
Area
of Triangle
= ½bh2
Area of Triangle 2 = ½bh
h
AREA OF A TRAPEZOID
Area of a trapezoid is
equal to the sum of the
areas of two triangles.
b1
I
II
b2
A= Triangle 1 + Triangle 2
A= ½bh + ½bh
A =½h(b+ b)
h
In the figure, b1 & b2
are the bases and h
is the height. Thus,
A= ½h( b1 + b2 )
b1
h
b2
In the figure, h = 8 cm,
b1 & b2 are 4 cm &
10 cm respectively.
Find the area of a
trapezoid.
b1
h
b2
Solution:
A =½h(b+ b)
4 cm
= ½(8 cm)(4 cm+ 10 cm)
= ½(8 cm)(14 cm)
= (4cm)(14 cm)
A = 56 cm²
8 cm
10 cm
How much do you
know
Find the area of the following:
1. A square with side of 25cm.
2. A parallelogram with base 17 m and
height 14 m.
3. A triangle with base equal to 12 cm
and altitude equal to 10 cm.
4. A rectangle 17m by 11m.
5. A trapezoid with height 6 cm and
the length of the bases are 7 cm and 9
cm.
Find the area of the following
figures.
1. A = s²

= (25 cm) ²
 A = 625 cm²

2. A = bh

= (17 m)(14 m)
 A = 238 m²

3. A = ½bh

= ½ (12 cm)(10 cm)

= (6 cm )(10 cm)

A = 60 cm²

Find the area of the following
figures.
4. A = lw

= (17 m) (11 m)
 A = 187 m²

 5. A = ½h(b1 + b2)



= ½ (6cm)(7 cm + 9 cm)
= (3 cm )(16 cm)
A =48 cm²
Let’s
Summarize
MAJOR CONCEPTS
1. The area of a region is the number
of square units contained in the
region.
2. A square unit is a square with a side
one (1) unit in length.
3. The area (A) of a rectangle is the
product of its length (l) and its width
(w).Thus,
A = lw
MAJOR CONCEPTS
4. The area (A) of a square is the
square of the length of a side (s).
A = s2
5. The area (A) of a parallelogram
is equal to the product of the
base (b) and the height (h).
Thus,
A = bh
MAJOR CONCEPTS
6. The diagonal separates the
parallelogram into two congruent
triangles.
7. The area (A) of a triangle equals
half the product of the base (b) and
the height (h). Thus, A = ½bh.
Sometimes altitude is used instead of
height.
MAJOR CONCEPTS
8. The area (A) of a trapezoid is
one half the product of
the
length of its altitude
and the sum of the lengths
of two
bases. Thus,
A = ½h (b1 + b2).