Input one known parameter: side length, height, perimeter, or area, and instantly calculate the height, perimeter, and area of an equilateral triangle.
Height (\( h \)): \( h = \frac{\sqrt{3}}{2} \times a \)
Perimeter (\( P \)): \( P = 3 \times a \)
Area (\( A \)): \( A = \frac{\sqrt{3}}{4} \times a^2 \)
Side Length (\( a \)): \( a = \frac{2h}{\sqrt{3}} \)
Perimeter (\( P \)): \( P = 3 \times a = 2\sqrt{3}h \)
Area (\( A \)): \( A = \frac{\sqrt{3}}{4} \times a^2 = \frac{h^2}{\sqrt{3}} \)
Side Length (\( a \)): \( a = \frac{P}{3} \)
Height (\( h \)): \( h = \frac{\sqrt{3}}{2} \times a = \frac{P}{2\sqrt{3}} \)
Area (\( A \)): \( A = \frac{\sqrt{3}}{4} \times a^2 = \frac{P^2}{12\sqrt{3}} \)
Side Length (\( a \)): \( a = \sqrt{\frac{4A}{\sqrt{3}}} \)
Height (\( h \)): \( h = \frac{\sqrt{3}}{2} \times a = \sqrt{\sqrt{3}A} \)
Perimeter (\( P \)): \( P = 3 \times a = 6 \times \sqrt{\frac{A}{\sqrt{3}}} \)
Solution:
Height:
\(h = \frac{\sqrt{3}}{2} \times 10 \approx 8.66\)
Perimeter:
\(P = 3 \times 10 = 30\)
Area:
\(A = \frac{\sqrt{3}}{4} \times 10^2 \approx 43.3\)
Solution:
Side Length:
\( a = \frac{2 \times 6}{\sqrt{3}} \approx 6.93 \)
Perimeter:
\( P = 3 \times 6.93 \approx 20.79 \)
Area:
\( A = \frac{\sqrt{3}}{4} \times 6.93^2 \approx 20.79 \)
Solution:
Side Length:
\( a = \frac{36}{3} = 12 \)
Height:
\( h = \frac{\sqrt{3}}{2} \times 12 \approx 10.39 \)
Area:
\( A = \frac{\sqrt{3}}{4} \times 12^2 \approx 62.35 \)
Solution:
Side Length:
\( a = \sqrt{\frac{4 \times 100}{\sqrt{3}}} \approx 15.19 \)
Height:
\( h = \frac{\sqrt{3}}{2} \times 15.19 \approx 13.15 \)
Perimeter:
\( P = 3 \times 15.19 \approx 45.59 \)