If you know the perimeter, then just divide it by 6 to get the length of one side. For example, if the length of the perimeter is 54 cm, then divide it by 6 to get 9 cm, the length of the side. [2] X Research source If you only know the apothem, you can find the length of a side by plugging the apothem into the formula a = x√3 and then multiplying the answer by two. This is because the apothem represents the x√3 side of the 30-60-90 triangle that it creates. If the apothem is 10√3, for example, then x is 10 and the length of a side is 10 * 2, or 20.
(3√3 x 92)/2 = (3√3 x 81)/2 = (243√3)/2 = 420. 8/2 = 210. 4 cm2
The apothem is the side that is represented by x√3. Therefore, plug the length of the apothem into the formula a = x√3 and solve. If the apothem’s length is 5√3, for example, plug it into the formula and get 5√3 cm = x√3, or x = 5 cm. By solving for x, you have found the length of the short leg of the triangle, 5. Since it represents half the length of one side of the hexagon, multiply it by 2 to get the full length of the side. 5 cm x 2 = 10 cm. Now that you know that the length of one side is 10, just multiply it by 6 to find the perimeter of the hexagon. 10 cm x 6 = 60 cm
Area = 1/2 x perimeter x apothem Area = 1/2 x 60 cm x 5√3 cm
1/2 x 60 cm x 5√3 cm = 30 x 5√3 cm = 150√3 cm = 259. 8 cm2
A: (4, 10) B: (9, 7) C: (11, 2) D: (2, 2) E: (1, 5) F: (4, 7) A (again): (4, 10)
4 x 7 = 28 9 x 2 = 18 11 x 2 = 22 2 x 5 = 10 1 x 7 = 7 4 x 10 = 40 28 + 18 + 22 + 10 + 7 + 40 = 125
10 x 9 = 90 7 x 11 = 77 2 x 2 = 4 2 x 1 = 2 5 x 4 = 20 7 x 4 = 28 90 + 77 + 4 + 2 + 20 + 28 = 221
For example, if you’ve found that the area of the regular hexagon is 60 cm2 and you’ve found that the area of the missing triangle is 10 cm2 simply subtract the area of the missing triangle from the entire area: 60 cm2 - 10 cm2 = 50 cm2. If you know that the hexagon is missing exactly one triangle, you can also just find the area of the hexagon by multiplying the total area by 5/6, since the hexagon is retaining the area of 5 of its 6 triangles. If it’s missing two triangles, you can multiply the total area by 4/6 (2/3), and so on.
One type of irregular hexagon is comprised of two parallelograms. To get the areas of the parallelograms, just multiply their bases times their heights, just as you would do to find the area of a rectangle, and then add up their areas.
