Triangles
Triangles
Area:
Area = 1/2 * base * height
Heron's formula:
s = (a+b+c)/2
Area = sqrt[s(s-a)(s-b)(s-c)]
Special triangles:
| Triangle | Side ratio |
|---|---|
| 30-60-90 | 1 : sqrt(3) : 2 |
| 45-45-90 | 1 : 1 : sqrt(2) |
| 3-4-5 | right triangle |
| 5-12-13 | right triangle |
| 7-24-25 | right triangle |
| 8-15-17 | right triangle |
Equilateral triangle:
Area = sqrt(3)/4 * a^2
Height = sqrt(3)/2 * a
Inradius = a/(2sqrt(3))
Circumradius = a/sqrt(3)
Similarity:
If two triangles are similar:
Side ratio = a:b
Area ratio = a^2:b^2
Volume ratio for similar solids = a^3:b^3
Median and centroid:
Centroid divides median in ratio 2:1 from vertex.
Median to hypotenuse in right triangle = half of hypotenuse.
Angle bisector:
Angle bisector divides opposite side in ratio of adjacent sides.