GEOMETRY – Area of Triangles

1
GEOMETRY Area of Triangles Lets take a look
first at the area of a right triangle. Recall, a
right triangle contains a 90 degree or right
angle. Its area is easily calculated.
2
GEOMETRY Area of Triangles Lets take a look
first at the area of a right triangle. Recall, a
right triangle contains a 90 degree or right
angle. Its area is easily calculated.
The height and base will ALWAYS be the sides that
create the right angle. They are interchangeable
which means you could switch the labels
height
base
3
GEOMETRY Area of Triangles Lets take a look
first at the area of a right triangle. Recall, a
right triangle contains a 90 degree or right
angle. Its area is easily calculated.
The height and base will ALWAYS be the sides that
create the right angle. They are interchangeable
which means you could switch the labels
height
base
If you cut a rectangle in half, you get 2 right
triangles.
4
GEOMETRY Area of Triangles Lets take a look
first at the area of a right triangle. Recall, a
right triangle contains a 90 degree or right
angle. Its area is easily calculated.
The height and base will ALWAYS be the sides that
create the right angle. They are interchangeable
which means you could switch the labels
height
base
If you cut a rectangle in half, you get 2 right
triangles. So each triangle would be half of the
rectangles area.
5
GEOMETRY Area of Triangles Lets take a look
first at the area of a right triangle. Recall, a
right triangle contains a 90 degree or right
angle. Its area is easily calculated.
The height and base will ALWAYS be the sides that
create the right angle. They are interchangeable
which means you could switch the labels
height
base
This is how we get the formula for the area of a
right triangle
6
GEOMETRY Area of Triangles
EXAMPLE 1 Find the area of the given
triangle
10 ft
4 ft
7
GEOMETRY Area of Triangles
EXAMPLE 1 Find the area of the given
triangle
10 ft
4 ft
8
GEOMETRY Area of Triangles
EXAMPLE 2 Find the area of the given
triangle
32 m
25 m
9
GEOMETRY Area of Triangles
EXAMPLE 2 Find the area of the given
triangle
32 m
25 m
10
GEOMETRY Area of Triangles
EXAMPLE 3 Find the base of the given
triangle
x
A 225 sq ft
28 ft
11
GEOMETRY Area of Triangles
EXAMPLE 3 Find the base of the given
triangle
x
A 225 sq ft
28 ft
Any decimal answer gets rounded to 2 decimal
places
12
GEOMETRY Area of Triangles Because we also
have acute and obtuse triangles, we need a way to
calculate their areas. We will look for an
altitude to use as the height. It makes sense,
altitude is how high something is off the ground
or base. The altitude will always create a 90
degree angle with the base
Acute
Obtuse
altitude
base
base
13
GEOMETRY Area of Triangles Because we also
have acute and obtuse triangles, we need a way to
calculate their areas. We will look for an
altitude to use as the height. It makes sense,
altitude is how high something is off the ground
or base. The altitude will always create a 90
degree angle with the base
Acute
Obtuse
altitude
base
base
The formula for area is still the same
14
GEOMETRY Area of Triangles EXAMPLE
Find the area of the given triangle
10 m
9 m
altitude height
15
GEOMETRY Area of Triangles EXAMPLE
Find the area of the given triangle
10 m
9 m
altitude height
16
GEOMETRY Area of Triangles EXAMPLE 2
Find the area of the given triangle
16 in.
11 in.
altitude height
17
GEOMETRY Area of Triangles EXAMPLE 2
Find the area of the given triangle
16 in.
11 in.
altitude height
18
GEOMETRY Area of Triangles
The last type of triangle we need to look at is
an equilateral triangle. Equilateral triangles
have equal sides AND angles ( all 60 degrees ).
60
S
S
60
60
S
19
GEOMETRY Area of Triangles
The last type of triangle we need to look at is
an equilateral triangle. Equilateral triangles
have equal sides AND angles ( all 60 degrees
). If we draw an altitude anywhere in our
triangle, we create two 30 60 90 triangles.
We also cut one sides distance in half.
60
S
S
60
60
S
20
GEOMETRY Area of Triangles
The last type of triangle we need to look at is
an equilateral triangle. Equilateral triangles
have equal sides AND angles ( all 60 degrees
). If we draw an altitude anywhere in our
triangle, we create two 30 60 90 triangles.
We also cut one sides distance in half.
60
Recall in a 30 60 90 triangle the medium
length side is the square root of three times
larger than the smallest side.
S
S
60
60
S
21
GEOMETRY Area of Triangles
The last type of triangle we need to look at is
an equilateral triangle. Equilateral triangles
have equal sides AND angles ( all 60 degrees
). If we draw an altitude anywhere in our
triangle, we create two 30 60 90 triangles.
We also cut one sides distance in half.
60
Since the sort side the middle side or the
altitude would be
S
S
60
60
S
22
GEOMETRY Area of Triangles
The last type of triangle we need to look at is
an equilateral triangle. Equilateral triangles
have equal sides AND angles ( all 60 degrees
). If we draw an altitude anywhere in our
triangle, we create two 30 60 90 triangles.
We also cut one sides distance in half.
60
Using the original formula using an altitude we
can now find the formula for the area of an
equilateral triangle
S
S
height
60
60
S
base
23
GEOMETRY Area of Triangles
Area of Equilateral triangles
EXAMPLE Find the area of an equilateral
triangle with sides of 12
12
12
12
24
GEOMETRY Area of Triangles
Area of Equilateral triangles
EXAMPLE Find the area of an equilateral
triangle with sides of 12
12
12
12