Math Area of a Triangle 1
directions:
Scrutinize each slide carefully, and you will do well.
Welcome Rutherford
County Students to the
Area of
triangle lesson
and quiz.

My name is MizzterG and I hope
this lesson helps you!
Triangles are three sided polygons.
There are many ways to classify them,
but that's another lesson.
The great thing about finding the area of a triangle
is that you really only need to know two things.
3 cm
height
If you know the base and the height of the triangle,
you will be able to find the area.
The key is to already know how to find the
area of a rectangle.
4 cm
base
comma
Remember that the formula for the area of a
rectangle is length times width.
A=  L x  W
The area of this rectangle is four times three.  You
can also multiply three times four since
multiplication is commutative.
3
A=  L x  W
4
3 x 4 =
Type in an answer.
square units
Now that you remember the formula for the
area of a rectangle, lets drop that triangle
on top .
3
A=  L x  W
4
There we go.  As you can see, the triangle only
covers part of the rectangle.  As a matter of fact, it
only covers half of it!
3
A =  L x  W
4
That means this
formula won't work
for a triangle.
What's the formula that will work for the area of a
triangle you ask.  Hmmm?
3
A =  L x  W
4
3 x 4 = 12
Well, since the triangle only covers half of the
rectangle, just take half of the answer for the
area of the rectangle and you've got it!
3
4
3
½
of the length times width
Well, since the triangle only covers half of the
rectangle, just take half of the answer for the
area of the rectangle and you've got it!
4
½
x 3 x 4
3
Multiply the length times the width and then just
divide by two.
½
of the length times width
4
3 x 4
2
=
½
x 3 x 4
square units
3 x 4
2
=
6
square units
If you answered this,
you got it right!
A=
We can write the formula for the area of a
triangle in a few ways:
½
b x h
A=
b x h
2
They all mean the same
thing.  Start like you are
getting the area of a
rectangle, then divide
by two.
A=
1
2
bh
Obviously, the areas of these two shapes can't be the
same.  If you look carefully, you see the triangle is
half of the rectangle.
4cm
2cm
4cm
2cm
The same amount of squares are not shaded.  Use
the formulas to find the areas.
4cm
2cm
4cm
2cm
Area of a rectangle      A= L x W
Area of a triangle      A= ½ x L x W or half L x W
4cm
2cm
4cm
2cm
4cm
A=
sq. units
2cm
4cm
This one is half of the other!!!!
A=
2cm
sq. units
4cm
A=
8
sq. units
ANSWERS
2cm
4cm
This one is half of the other!!!!
A=
2cm
4
sq. units
Let's try a demonstration in case you didn't get it.
Click on the next few slids to see me chop the
rectangle in half.  That way, you will see how the
formula works.
4mm
A=
5mm
mm2
Here is a rectangle.

A= L x W
4mm
A=
20
5mm
mm2
Now let's chop it in half.
answer
HI-SA!
4mm
Area of both triangles together
5mm
The area of the two triangles
together has not changed.
mm2
4mm
Area of both triangles together
5mm
The area of the two triangles
together has not changed.
20
mm2
4mm
5mm
Area of just this triangle?
Remember, half of the base
times the height.
mm2
4mm
5mm
Area of just this triangle?
Remember, half of the base
times the height.
mm2
don't worry about
this side.
5mm
4mm
4mm
10
5mm
Each half of the rectangle
is 10mm2
mm2
Together they are 20 mm2
10
5mm
mm2
4mm
Area of a triangle =
Area of a triangle =
b x h
b x
Area of a triangle =
quiz time!
1
2
b x h
10 ft
8 ft
ft2
A = ½ b x h
4cm
4cm
cm2
8cm
4cm
cm2
cm2
3cm
10cm
mm
1
A=
20
20
mm
mm2
mm
A=
mm2
2
mm
Hmm?  This triangle looks a bit different.  Don't
panic.  Just remember the formula. ½ b  x h.
This triangle has a base of 10 mm.
This triangle has a base of 10 mm.
One side is 8 mm.
The third side is 9 mm.
Don't let these two
trick you.
We must have
the height.
8mm
10mm
9mm
The height is 7 mm.
The height of this triangle is from it's tallest point
to the base.  You have to measure in the middle.
½ 7x 10=
So to find the area of this triangle, you would use
½ b x h     or   ½ 7 x 10.
mm2
8mm
7mm
10mm
9mm
½ 7x 10=
Answer
70
Don't let the other sides distract you.  You must
use the base and the height only.
2
35
mm2
8mm
7mm
10mm
9mm
10mm
5mm
13mm
Make sure you pick the base
and the height before dividing
by 2.
10mm
5mm
A =
13mm
mm2
10mm
5mm
A =
13mm
½
5x10
50
2
= 25
mm2
answer
12cm
8cm
5cm
11cm
use the base
and height!
A =
cm2
distracter
8x5
2
base
=
12cm
40
2
height
=
8cm
5cm
20
distracter
11cm
use the base
and height!
A =
20
cm2
7cm
9cm
4cm
6cm
use the base
and height!
A =
cm2
don't forget to
divide by 2
7cm
3cm
20cm
15cm
use the base
and height!
A =
cm2
don't forget to
divide by 2
See you soon!
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