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Exploring Area and Surface Area
Mathematics, Grade 7
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Study Guide Exploring Area and Surface Area Mathematics, Grade 7
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4
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EXPLORING
AREA
AND
SURFACE
AREA
Area
is
the
amount
of
surface
a
shape
covers.
Area
is
measured
in
square
units,
whether
the
units
are
inches,
feet,
meters
or
centimeters.
•
The
area
formula
for
a
triangle
is:
A
=
1/2
·
b
·
h,
where
b
is
the
base
and
h
is
the
height.
•
The
area
formula
for
a
circle
is:
A
=
π
·
r²,
where
π
is
usually
3.14
and
r
is
the
radius
of
the
circle.
•
The
area
formula
for
a
parallelogram
is:
A
=
b
·
h,
where
b
is
the
base
and
h
is
the
height.
•
The
area
of
a
trapezoid
is:
A
=
(1/2)(b1
+
b2)
·
h,
where
b1
is
one
base
and
b2
is
the
other
base
and
h
is
the
height.
Surface
area
is
the
sum
of
all
the
areas
of
the
surfaces
of
an
object.
•
The
surface
area
of
a
rectangular
prism
is:
SA
=
2wl
+
2lh
+
2
hw.
•
The
surface
area
of
a
triangular
prism
is:
SA
=
wl
+
lh
+
hw
+
bh.
•
The
surface
area
of
a
cylinder
is:
SA
=
2π
r
·
h
+
2π
r².
The
surface
area
of
a
sphere
is:
SA
=
4π
r².
For
the
surface
area
of
a
cylinder
and
a
sphere,
π
is
usually
3.14.
•
A
net
of
a
figure
is
simply
a
flat
pattern
of
the
figure
that
when
folded
would
form
a
solid
figure.
When
comparing
two
similar
figures,
their
surface
areas
should
be
in
proportion
to
each
other.
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Permission
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granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
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www.NewPathLearning.com.
How
to
use
exploring
area
and
surface
area
The
area
of
any
figure
can
be
found
if
given
the
appropriate
dimensions.
•
For
example,
to
find
the
area
of
a
triangle,
use
the
formula
A
=
1/2
· b
· h
,
and
fill
in
the
base
and
the
height.
Then
multiply
the
base
and
height
together
and
divide
by
two
to
find
the
area.
•
If
the
area
of
a
triangle
and
one
side
of
the
triangle
is
given,
the
missing
side
can
be
found
by
using
the
same
formula.
This
time
the
area
will
be
filled
in
as
well
as
either
the
base
or
the
height,
depending
on
what
is
given.
•
By
performing
the
operations,
the
result
will
be
the
missing
side.
Finding
a
missing
side
or
diameter
can
be
done
with
any
shape
and
the
area
formulas
for
that
shape.
•
For
example,
what
is
the
radius
of
a
circle
with
an
area
of
78.5
units²?
Ex.
Area
=
78.5
units²
A
=
π
·
r²
78.5
=
3.14
· r
²
3.14
3.14
25
=
r²
5
=
r
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
The
surface
area
of
any
figure
can
be
found
using
the
appropriate
formulas.
For
example,
what
is
the
surface
area
of
a
sphere
with
a
radius
of
5
inches?
Ex.
SA
sphere
=
4π
r²
=
(4)(3.14)(5²)
=
(4)(3.14)(25)
=
314
inches²
If
the
surface
area
and
all
other
dimensions
are
given
except
one
dimension,
the
missing
dimension
can
be
found
by
plugging
in
the
surface
area
and
given
dimensions
and
solving
for
the
missing
dimension.
Try
This!
1.
What
is
the
area
of
a
rectangle
with
a
base
of
3
m
and
a
height
of
5
m?
2.
What
is
the
area
of
the
triangle
with
a
base
of
4
cm
and
a
height
of
12
cm?
3.
What
is
the
area
of
the
circle
with
a
diameter
of
14
inches?
4.
What
is
the
area
of
a
trapezoid
with
bases,
2
ft
and
4
ft,
and
a
height
of
5
ft?
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
5.
What
is
the
missing
side
of
a
rectangle
with
an
area
of
64
m²
and
a
base
of
4m?
6.
What
is
the
base
of
a
triangle
with
an
area
of
39
m²
and
a
height
of
13
m?
7.
What
is
the
radius
of
a
circle
with
an
area
of
28.26
cm²?
8.
What
is
the
surface
area
of
a
rectangle
with
a
length
of
2
cm,
a
width
of
3
cm
and
a
height
of
5
cm?
9.
What
is
the
surface
area
of
a
cylinder
with
a
radius
of
12
in.
and
a
height
of
24
in.?
10.
What
is
the
surface
area
of
a
sphere
with
a
diameter
of
10
ft?
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
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