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GEOMETRY – Area of Triangles Let’s take a look first at the area of a right triangle. Recall, a right triangle contains a 90 degree or “right” angle. It’s area is easily calculated.
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GEOMETRY – Area of Triangles
Let’s take a look first at the area of a right triangle. Recall, a right triangle contains a 90 degree or “right” angle. It’s area is easily calculated.
GEOMETRY – Area of Triangles
Let’s take a look first at the area of a right triangle. Recall, a right triangle contains a 90 degree or “right” angle. It’s area is easily calculated.
height
The height and base will ALWAYS be the sides that create the right angle. They are interchangeable which means you could switch the labels…
base
GEOMETRY – Area of Triangles
Let’s take a look first at the area of a right triangle. Recall, a right triangle contains a 90 degree or “right” angle. It’s area is easily calculated.
height
The height and base will ALWAYS be the sides that create the right angle. They are interchangeable which means you could switch the labels…
base If you cut a rectangle in half, you get 2 right triangles.
GEOMETRY – Area of Triangles
Let’s take a look first at the area of a right triangle. Recall, a right triangle contains a 90 degree or “right” angle. It’s area is easily calculated.
height
The height and base will ALWAYS be the sides that create the right angle. They are interchangeable which means you could switch the labels…
base If you cut a rectangle in half, you get 2 right triangles.
So each triangle would be half of the rectangles area.
lwa2
1
lwa2
1
GEOMETRY – Area of Triangles
Let’s take a look first at the area of a right triangle. Recall, a right triangle contains a 90 degree or “right” angle. It’s area is easily calculated.
height
The height and base will ALWAYS be the sides that create the right angle. They are interchangeable which means you could switch the labels…
base
This is how we get the formula for the area of a right triangle…
lwa2
1
lwa2
1
bharea2
1
GEOMETRY – Area of Triangles
10 ft
4 ft
bharea2
1
EXAMPLE # 1 : Find the area of the given triangle :
GEOMETRY – Area of Triangles
10 ft
4 ft
bharea2
1
EXAMPLE # 1 : Find the area of the given triangle :
feet square 20
4102
12
1
a
a
bha
GEOMETRY – Area of Triangles
25 m
32 m
bharea2
1
EXAMPLE # 2 : Find the area of the given triangle :
GEOMETRY – Area of Triangles
25 m
32 m
bharea2
1
EXAMPLE # 2 : Find the area of the given triangle :
meters sq. 400
32252
1
a
a
GEOMETRY – Area of Triangles
28 ft
x
bharea2
1
EXAMPLE # 3 : Find the base of the given triangle :
A = 225 sq ft
GEOMETRY – Area of Triangles
28 ft
x
bharea2
1
EXAMPLE # 3 : Find the base of the given triangle :
A = 225 sq ft
07.16
14225
282
1225
x
x
x
Any decimal answer gets rounded to 2 decimal places…
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
AcuteObtuse
basebase
altitude
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
AcuteObtuse
basebase
altitude
bha2
1 The formula for area is
still the same…
GEOMETRY – Area of Triangles
EXAMPLE : Find the area of the given triangle :
10 m
9 m
bha2
1
altitude = height
GEOMETRY – Area of Triangles
EXAMPLE : Find the area of the given triangle :
10 m
9 m
bha2
1
altitude = height
meters sq. 45
1092
1
a
a
GEOMETRY – Area of Triangles
EXAMPLE # 2 : Find the area of the given triangle :
16 in.
11 in.
bha2
1
altitude = height
GEOMETRY – Area of Triangles
EXAMPLE # 2 : Find the area of the given triangle :
16 in.
11 in.
bha2
1
altitude = height
inches sq. 88
16112
1
a
a
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 60
60
S
S
S
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 60
60
S
S
S
S2
1
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 60
60
S
S
S
S2
1
Recall in a 30 – 60 – 90 triangle the medium length side is the square root of three times larger than the smallest side.
3s
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 60
60
S
S
S
S2
1
Since the sort side =
the middle side or the altitude would be :2
3s
s2
1
2
33
2
1 ss
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 60
60
S
S
S
Using the original formula using an altitude we can now find the formula for the area of an equilateral triangle :2
3s height
base
4
3
2
3
12
1
2
1
2Sa
SSa
bha
GEOMETRY – Area of Triangles
Area of Equilateral triangles :
12
12
12
4
32Sa
EXAMPLE : Find the area of an equilateral triangle with sides of 12 :
GEOMETRY – Area of Triangles
Area of Equilateral triangles :
12
12
12
4
32Sa
EXAMPLE : Find the area of an equilateral triangle with sides of 12 :
3364
3144
4
312 2
a
a
