Question

Find the area of rectangle hexagon of side 19 cm

Answer 1

Step-by-step explanation:

Write down the formula for finding the area of a hexagon if you know the side length. Since a regular hexagon is comprised of six equilateral triangles, the formula for finding the area of a hexagon is derived from the formula of finding the area of an equilateral triangle. The formula for finding the area of a hexagon is Area = (3√3 s2)/ 2 where s is the length of a side of the regular hexagon.[1]

Image titled Calculate the Area of a Hexagon Step 2

2

Identify the length of one one side. If you already know the length of a side, then you can simply write it down; in this case, the length of a side is 9 cm. If you don't know the length of a side but know the length of the perimeter or apothem (the height of one of the equilateral triangles formed by the hexagon, which is perpendicular to the side), you can still find the length of the side of the hexagon. Here's how you do it:

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]

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.

Image titled Calculate the Area of a Hexagon Step 3

3

Plug the value of the side length into the formula. Since you know that the length of one side of the triangle is 9, just plug 9 into the original formula. It will look like this: Area = (3√3 x 92)/2

Image titled Calculate the Area of a Hexagon Step 4

4

Simplify your answer. Find the value of equation and write the numerical answer. Since you're working with area, you should state your answer in square units. Here's how you do it:

(3√3 x 92)/2 =

(3√3 x 81)/2 =

(243√3)/2 =

420.8/2 =

210.4 cm2