中间几何:六边形

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #141 :Hexagons

1

In the regular hexagon above, if the length of diagonalis, what is the area of the hexagon?

Possible Answers:

Correct answer:

Explanation:

14

当所有的对角线六边形的画,you should notice that the long diagonals, marked by solid lines, formcongruent 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 congruenttriangles 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 toplaces after the decimal.

Example Question #142 :Hexagons

1

In the regular hexagon above, if the length of diagonalis, what is the area of the hexagon?

Possible Answers:

Correct answer:

Explanation:

14

当所有的对角线六边形的画,you should notice that the long diagonals, marked by solid lines, formcongruent 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 congruenttriangles 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 toplaces after the decimal.

Example Question #143 :Hexagons

1

In the regular hexagon above, if the length of diagonalis, what is the area of the hexagon?

Possible Answers:

Correct answer:

Explanation:

14

当所有的对角线六边形的画,you should notice that the long diagonals, marked by solid lines, formcongruent 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 congruenttriangles 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 toplaces after the decimal.

Example Question #144 :Hexagons

1

In the regular hexagon above, if the length of diagonalis, what is the area of the hexagon?

Possible Answers:

Correct answer:

Explanation:

14

当所有的对角线六边形的画,you should notice that the long diagonals, marked by solid lines, formcongruent 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 congruenttriangles 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 toplaces after the decimal.

Example Question #145 :Hexagons

1

In the regular hexagon above, if diagonalhas a length of, what is the area of the hexagon?

Possible Answers:

Correct answer:

Explanation:

14

当所有的对角线六边形的画,you should notice that the long diagonals, marked by solid lines, formcongruent 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 congruenttriangles 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 toplaces after the decimal.

Example Question #146 :Hexagons

1

In the regular hexagon above, if diagonalhas a length of, what is the area of the hexagon?

Possible Answers:

Correct answer:

Explanation:

14

当所有的对角线六边形的画,you should notice that the long diagonals, marked by solid lines, formcongruent 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 congruenttriangles 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 toplaces after the decimal.

Example Question #147 :Hexagons

1

In the regular hexagon above, if diagonalhas a length of, what is the area of the hexagon?

Possible Answers:

Correct answer:

Explanation:

14

当所有的对角线六边形的画,you should notice that the long diagonals, marked by solid lines, formcongruent 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 congruenttriangles 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 toplaces after the decimal.

Example Question #148 :Hexagons

1

In the regular hexagon above, if diagonalhas a length of, what is the area of the hexagon?

Possible Answers:

Correct answer:

Explanation:

14

当所有的对角线六边形的画,you should notice that the long diagonals, marked by solid lines, formcongruent 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 congruenttriangles 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 toplaces after the decimal.

Example Question #149 :Hexagons

1

In the regular hexagon above, if diagonalis, what is the area of the hexagon?

Possible Answers:

Correct answer:

Explanation:

14

当所有的对角线六边形的画,you should notice that the long diagonals, marked by solid lines, formcongruent 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 congruenttriangles 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 toplaces after the decimal.

Example Question #150 :Hexagons

1

In the regular hexagon above, if diagonalhas a length of, what is the area of the hexagon?

Possible Answers:

Correct answer:

Explanation:

14

当所有的对角线六边形的画,you should notice that the long diagonals, marked by solid lines, formcongruent 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 congruenttriangles 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 toplaces after the decimal.

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