When all of the diagonals of a regular hexagon are drawn in, you should notice that the hexagon is divided into six congruent equilateral triangles. The length of the diagonal is twice the length of a side of one of the equilateral triangles.

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

Substitute in the given diagonal to find the side length of the hexagon.

Now, recall how to find the area of a regular hexagon.

Substitute in the value of the side length to find the area of the hexagon.

Next, notice that the hexagon shares a side with the length of the rectangle.

Recall how to find the area of a rectangle.

Substitute in the length and the width of the rectangle to find the area.

.

In order to find the area of the entire figure, add the areas of the hexagon and rectangle together.

Solve and round to two decimal places.

The following equation can be used to solve for area of a regular polygon, given the side length and number of sides :

We can solve for area using the given formula that works for all regular polygons, with being the side length and representing the number of sides:

When all the diagonals of a hexagon are drawn in, you should notice that the long diagonals, marked by solid lines, form  congruent equilateral triangles. You should also notice that the other diagonals drawn in with dashed lines are also the heights of two of the equilateral triangles.

Start by using the diagonal to find the length of a side of the hexagon.

Cut the diagonal in half so that we are just left with the height of one equilateral triangle. Notice that the height cleaves the equilateral triangle into two congruent  triangles whose sides are in the ratios of .

Set up a proportion to solve for the length of a side of the triangle.

Plug in the given diagonal to solve for the side length.

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

Plug in the side length that you just found in order to find the area.

Make sure to round to  places after the decimal.

When all the diagonals of a hexagon are drawn in, you should notice that the long diagonals, marked by solid lines, form  congruent equilateral triangles. You should also notice that the other diagonals drawn in with dashed lines are also the heights of two of the equilateral triangles.

Start by using the diagonal to find the length of a side of the hexagon.

Cut the diagonal in half so that we are just left with the height of one equilateral triangle. Notice that the height cleaves the equilateral triangle into two congruent  triangles whose sides are in the ratios of .

Set up a proportion to solve for the length of a side of the triangle.

Plug in the given diagonal to solve for the side length.

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

Plug in the side length that you just found in order to find the area.

Make sure to round to  places after the decimal.

When all the diagonals of a hexagon are drawn in, you should notice that the long diagonals, marked by solid lines, form  congruent equilateral triangles. You should also notice that the other diagonals drawn in with dashed lines are also the heights of two of the equilateral triangles.

Start by using the diagonal to find the length of a side of the hexagon.

Cut the diagonal in half so that we are just left with the height of one equilateral triangle. Notice that the height cleaves the equilateral triangle into two congruent  triangles whose sides are in the ratios of .

Set up a proportion to solve for the length of a side of the triangle.

Plug in the given diagonal to solve for the side length.

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

Plug in the side length that you just found in order to find the area.

Make sure to round to  places after the decimal.

When all the diagonals of a hexagon are drawn in, you should notice that the long diagonals, marked by solid lines, form  congruent equilateral triangles. You should also notice that the other diagonals drawn in with dashed lines are also the heights of two of the equilateral triangles.

Start by using the diagonal to find the length of a side of the hexagon.

Cut the diagonal in half so that we are just left with the height of one equilateral triangle. Notice that the height cleaves the equilateral triangle into two congruent  triangles whose sides are in the ratios of .

Set up a proportion to solve for the length of a side of the triangle.

Plug in the given diagonal to solve for the side length.

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

Plug in the side length that you just found in order to find the area.

Make sure to round to  places after the decimal.

When all the diagonals of a hexagon are drawn in, you should notice that the long diagonals, marked by solid lines, form  congruent equilateral triangles. You should also notice that the other diagonals drawn in with dashed lines are also the heights of two of the equilateral triangles.

Start by using the diagonal to find the length of a side of the hexagon.

Cut the diagonal in half so that we are just left with the height of one equilateral triangle. Notice that the height cleaves the equilateral triangle into two congruent  triangles whose sides are in the ratios of .

Set up a proportion to solve for the length of a side of the triangle.

Plug in the given diagonal to solve for the side length.

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

Plug in the side length that you just found in order to find the area.

Make sure to round to  places after the decimal.

When all the diagonals of a hexagon are drawn in, you should notice that the long diagonals, marked by solid lines, form  congruent equilateral triangles. You should also notice that the other diagonals drawn in with dashed lines are also the heights of two of the equilateral triangles.

Start by using the diagonal to find the length of a side of the hexagon.

Cut the diagonal in half so that we are just left with the height of one equilateral triangle. Notice that the height cleaves the equilateral triangle into two congruent  triangles whose sides are in the ratios of .

Set up a proportion to solve for the length of a side of the triangle.

Plug in the given diagonal to solve for the side length.

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

Plug in the side length that you just found in order to find the area.

Make sure to round to  places after the decimal.

When all the diagonals of a hexagon are drawn in, you should notice that the long diagonals, marked by solid lines, form  congruent equilateral triangles. You should also notice that the other diagonals drawn in with dashed lines are also the heights of two of the equilateral triangles.

Start by using the diagonal to find the length of a side of the hexagon.

Cut the diagonal in half so that we are just left with the height of one equilateral triangle. Notice that the height cleaves the equilateral triangle into two congruent  triangles whose sides are in the ratios of .

Set up a proportion to solve for the length of a side of the triangle.

Plug in the given diagonal to solve for the side length.

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

Plug in the side length that you just found in order to find the area.

Make sure to round to  places after the decimal.