Geometry - How to find the perimeter of a hexagon

Find the perimeter of the regular hexagon.

Explanation

When all the opposite sides of a regular hexagon are connected, you should notice that six congruent equilateral triangles are created:

Thus, the diagonal of the hexagon is twice the length of a side.

$\text{Diagonal}=2(\text{side})$

$\text{Side}=\frac{\text{Diagonal}}{2}$

Plug in the given diagonal to find the length of a side.

$\text{Side}=\frac{14}{2}=7$

Now, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Plug in the side length to find the perimeter.

$\text{Perimeter}=6(7)=42$

If the area of a regular hexagon is $15\sqrt3$ , what is the perimeter of the hexagon?

Explanation

Recall the formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}(\text{side})^2$

Rearrange the formula to solve for the side.

$(\text{side})^2=\text{Area}(\frac{2}{3\sqrt3})$

$\text{side}=\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Now, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Substitute in for the side to solve for the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Plug in the given area and use a calculator to find the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(15\sqrt3)}{3\sqrt3}}=18.97$

Make sure to round to the two places after the decimal.

What is the perimeter of a hexagon if a side length is ?

Explanation

A hexagon has 6 sides.

Given the length of the side is 100, the perimeter is:

$P=6s = 6\cdot100 =600$

If the area of a regular hexagon is , what is the perimeter of the hexagon?

Explanation

Recall the formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}(\text{side})^2$

Rearrange the formula to solve for the side.

$(\text{side})^2=\text{Area}(\frac{2}{3\sqrt3})$

$\text{side}=\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Now, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Substitute in for the side to solve for the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Plug in the given area and use a calculator to find the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(25)}{3\sqrt3}}=18.61$

Make sure to round to the two places after the decimal.

Find the perimeter of the regular hexagon below:

$28\sqrt3$

$35\sqrt3$

$21\sqrt3$

$14\sqrt3$

Explanation

When all the diagonals of the regular hexagon are drawn in, you should notice that six congruent equilateral triangles are created.

Thus, we know that the given line segment, also known as an apothem, acts as the height of an equilateral triangle. The apothem also creates two congruent triangles.

Thus, we can use the ratio of the side lengths to find the length of the base of one of the triangles.

Recall that the ratios of the side lengths in a triangle are $1:\sqrt3:2$ .

We can then set up the following equation:

$\frac{7}{\sqrt3}=\frac{\text{base}}{1}$

The length of the base is then $\frac{7}{\sqrt3}=\frac{7\sqrt3}{3}$ .

Now, the length of this base is half the length of a side of the hexagon. Multiply the base by two to find the length of a side:

$\text{side}=2(\text{base})$

$\text{side}=2(\frac{7\sqrt3}{3})=\frac{14\sqrt3}{3}$

Next, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Plug in the side length to find the perimeter:

$\text{Perimeter}=6(\frac{14\sqrt3}{3})=28\sqrt3$

If the side of a hexagon has a length of , what is the perimeter of the hexagon?

Explanation

The perimeter of a hexagon is:

Substitute the side length and solve for the perimeter.

If the lengh of a side of a hexagon is $\frac{a}{2}$ , what is the perimeter?

$\frac{a}{12}$

$\frac{a}{6}$

Explanation

Write the formula for the perimeter of a hexagon.

Substitute the side and simplify.

$P=6\left(\frac{a}{2}\right)=3a$

Find the perimeter of the regular hexagon below:

$12\sqrt3$

$9\sqrt3$

$15\sqrt3$

$18\sqrt3$

Explanation

When all the diagonals of the regular hexagon are drawn in, you should notice that six congruent equilateral triangles are created.

Thus, we know that the given line segment, also known as an apothem, acts as the height of an equilateral triangle. The apothem also creates two congruent triangles.