### All Intermediate Geometry Resources

## Example Questions

### Example Question #21 : How To Find The Length Of The Diagonal Of A Hexagon

If the perimeter of the regular hexagon above is , find the length of diagonal .

**Possible Answers:**

**Correct answer:**

When the regular hexagon is divided into congruent equilateral triangles, it's easy to see that diagonal is comprised of two heights of two equilateral triangles. This holds true for the other diagonals when drawn in, as shown by dotted lines in the figure below:

Now, in order to find the length of the diagonal, we will need to first find the length of a side of the hexagon.

Plug in the given perimeter to find the length of a side for the given hexagon.

Notice that the height of the equilateral triangle creates two congruent triangles whose side lengths are in the ratio of .

Thus, we can set up the following proportion to find the length of the height:

Since the diagonal is made up of two of these heights, multiply by to find the length of the diagonal.

### Example Question #22 : How To Find The Length Of The Diagonal Of A Hexagon

If the perimeter of the regular hexagon above is , find the length of diagonal .

**Possible Answers:**

**Correct answer:**

When the regular hexagon is divided into congruent equilateral triangles, it's easy to see that diagonal is comprised of two heights of two equilateral triangles. This holds true for the other diagonals when drawn in, as shown by dotted lines in the figure below:

Now, in order to find the length of the diagonal, we will need to first find the length of a side of the hexagon.

Plug in the given perimeter to find the length of a side for the given hexagon.

Notice that the height of the equilateral triangle creates two congruent triangles whose side lengths are in the ratio of .

Thus, we can set up the following proportion to find the length of the height:

Since the diagonal is made up of two of these heights, multiply by to find the length of the diagonal.

### Example Question #23 : How To Find The Length Of The Diagonal Of A Hexagon

If the perimeter of the regular hexagon above is , find the length of diagonal .

**Possible Answers:**

**Correct answer:**

When the regular hexagon is divided into congruent equilateral triangles, it's easy to see that diagonal is comprised of two heights of two equilateral triangles. This holds true for the other diagonals when drawn in, as shown by dotted lines in the figure below:

Now, in order to find the length of the diagonal, we will need to first find the length of a side of the hexagon.

Plug in the given perimeter to find the length of a side for the given hexagon.

Notice that the height of the equilateral triangle creates two congruent triangles whose side lengths are in the ratio of .

Thus, we can set up the following proportion to find the length of the height:

Since the diagonal is made up of two of these heights, multiply by to find the length of the diagonal.

### Example Question #24 : How To Find The Length Of The Diagonal Of A Hexagon

If the perimeter of the regular hexagon above is , what is the length of diagonal ?

**Possible Answers:**

**Correct answer:**

Plug in the given perimeter to find the length of a side for the given hexagon.

Thus, we can set up the following proportion to find the length of the height:

### Example Question #25 : How To Find The Length Of The Diagonal Of A Hexagon

If the perimeter of the regular hexagon above is , what is the length of diagonal ?

**Possible Answers:**

**Correct answer:**

Plug in the given perimeter to find the length of a side for the given hexagon.

Thus, we can set up the following proportion to find the length of the height: