Step-by-step explanation:
Since an isosceles triangle has two equal sides, if the triangle is split in half vertically, the length of the base on each side is:
12
c
m
÷
2
=
6
c
m
We can then use the Pythagorean theorem to find the height of the triangle.
The formula for the Pythagorean theorem is:
a
2
+
b
2
=
c
2
To solve for the height, substitute your known values into the equation and solve for
a
:
where:
a
= height
b
= base
c
= hypotenuse
a
2
+
b
2
=
c
2
a
2
=
c
2
−
b
2
a
2
=
(
10
)
2
−
(
6
)
2
a
2
=
(
100
)
−
(
36
)
a
2
=
64
a
=
√
64
a
=
8
Now that we have our known values, substitute the following into the formula for area of a triangle:
b
a
s
e
=
12
c
m
h
e
i
g
h
t
=
8
c
m
A
r
e
a
=
b
a
s
e
⋅
h
e
i
g
h
t
2
A
r
e
a
=
(
12
)
⋅
(
8
)
2
A
r
e
a
=
96
2
A
r
e
a
=
48
∴
, the area is
48
c
m
2
.