# Intermediate Geometry : How to find the perimeter of a hexagon

## Example Questions

### Example Question #31 : Hexagons

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:

Rearrange the formula to solve for the side.

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

Substitute in for the side to solve for the perimeter.

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

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

### Example Question #32 : Hexagons

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:

Rearrange the formula to solve for the side.

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

Substitute in for the side to solve for the perimeter.

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

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

### Example Question #33 : Hexagons

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:

Rearrange the formula to solve for the side.

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

Substitute in for the side to solve for the perimeter.

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

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

### Example Question #34 : How To Find The Perimeter Of A Hexagon

Find the perimeter of the regular hexagon below.

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 .

We can then set up the following equation:

The length of the base is then .

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:

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

Plug in the side length to find the perimeter:

### Example Question #35 : How To Find The Perimeter Of A Hexagon

Find the perimeter of the regular hexagon below:

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 .

We can then set up the following equation:

The length of the base is then .

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:

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

Plug in the side length to find the perimeter:

### Example Question #36 : How To Find The Perimeter Of A Hexagon

Find the perimeter of the regular hexagon below:

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 .

We can then set up the following equation:

The length of the base is then .

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:

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

Plug in the side length to find the perimeter:

### Example Question #37 : How To Find The Perimeter Of A Hexagon

Find the perimeter of the regular hexagon below:

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 .

We can then set up the following equation:

The length of the base is then .

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:

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

Plug in the side length to find the perimeter:

### Example Question #38 : How To Find The Perimeter Of A Hexagon

Find the perimeter of the regular hexagon below:

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 .

We can then set up the following equation:

The length of the base is then .

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:

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

Plug in the side length to find the perimeter:

### Example Question #39 : How To Find The Perimeter Of A Hexagon

Find the perimeter of the regular hexagon below:

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 .

We can then set up the following equation:

The length of the base is then .

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:

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

Plug in the side length to find the perimeter:

### Example Question #40 : How To Find The Perimeter Of A Hexagon

Find the perimeter of the regular hexagon below:

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 .

We can then set up the following equation:

The length of the base is then .

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:

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

Plug in the side length to find the perimeter: