8
√
3
and
48
√
3
square cm
Explanation:
the altitude of an equilateral triangle 'splits' the
triangle into 2 congruent right triangles
let the side of the equilateral triangle
=
x
consider one right triangle
with hypotenuse
=
x
and legs
=
12
and
1
2
x
using
Pythagoras' theorem
x
2
=
(
1
2
x
)
2
+
12
2
⇒
x
2
=
1
4
x
2
+
144
⇒
3
4
x
2
=
144
⇒
x
2
=
(
144
×
4
3
)
=
192
⇒
x
=
√
192
=
8
√
3
←
exact value
area
=
1
2
×
8
√
3
×
12
=
48
√
3
←
exact value
