The diagonal of a square equals the side of an equilateral triangle. If the area of the square is 12 sq cm, what is the area of the equilateral triangle?
- A12
3
sq cm - B6
3
sq cm - C12
2
sq cm - D24 sq cm
Solution & Step-by-step Explanation
Let the side of the square be s and its diagonal be d.
Area of the square = s
2
=12 sq cm
The relationship between side and diagonal of a square is:
d=s
2
Squaring both sides:
d
2
=2s
2
=2×12=24
According to the problem, the side of the equilateral triangle (a) equals the diagonal of the square (d):
a=d⟹a
2
=d
2
=24
The area of an equilateral triangle is given by:
Area=
4
3
a
2
Area=
4
3
×24=6
3
sq cm
Area of the square = s
2
=12 sq cm
The relationship between side and diagonal of a square is:
d=s
2
Squaring both sides:
d
2
=2s
2
=2×12=24
According to the problem, the side of the equilateral triangle (a) equals the diagonal of the square (d):
a=d⟹a
2
=d
2
=24
The area of an equilateral triangle is given by:
Area=
4
3
a
2
Area=
4
3
×24=6
3
sq cm