Hexagons - ISEE Upper Level Quantitative Reasoning

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Question

The perimeter of a regular hexagon is one mile. Give the sidelength in feet.

Answer

One mile is equal to 5,280 feet, so divide this by 6:

$5,280 \div 6 = 880$ feet

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Question

What is the sidelength, in feet and inches, of a regular hexagon with perimeter 16 feet?

Answer

Divide the perimeter 16 feet by 6 to get the sidelength of the hexagon in feet:

$16 \div 6 = 2\frac{2}{3} \textrm{ ft }$

Two-thirds of a foot is equal to eight inches, so this sidelength is 2 feet 8 inches.

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Question

The perimeter of a hexagon is 96cm. Find the length of one side.

Answer

A hexagon has 6 equal sides. To find the length of one side of a hexagon, we will use the formula to find the perimeter.

where a is the length of one side. So, we will solve for a.

Now, we know the perimeter of the hexagon is 96cm. So, we get

$96\text{cm} = 6a$

$\frac{96\text{cm}}{6} = \frac{6a}{6}$

$16\text{cm} = a$

$a = 16\text{cm}$

Therefore, the length of one side of the hexagon is 16cm.

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Question

A hexagon has a perimeter of 114in. Find the length of one side.

Answer

A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is:

where a is the length of any side. Now, to find the length of one side, we will solve for a.

We know the perimeter of the hexagon is 114in. So, we will substitute and solve for a. We get

$114\text{in} = 6a$

$\frac{114\text{in}}{6} = \frac{6a}{6}$

$19\text{in} = a$

$a = 19\text{in}$

Therefore, the length of one side of the hexagon is 19in.

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Question

A regular hexagon has the same perimeter as the above right triangle. What is the length of one side of the hexagon?

Answer

By the Pythagorean Theorem, the hypotenuse of the right triangle is

$\sqrt{14^{2}+48^{2}} = \sqrt{196+2,304} = \sqrt{2,500} = 50$ inches, making its perimeter

inches.

The regular hexagon, which has six sides of equal length, has the same perimeter, so each side measures

$112 \div 6 = 18 \frac{2}{3}$ inches.

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Question

A regular hexagon has the same perimeter as the above right triangle. What is the length of one side of the hexagon?

Answer

By the Pythagorean Theorem, the hypotenuse of the right triangle is

$\sqrt{14^{2}+48^{2}} = \sqrt{196+2,304} = \sqrt{2,500} = 50$ inches, making its perimeter

inches.

The regular hexagon, which has six sides of equal length, has the same perimeter, so each side measures

$112 \div 6 = 18 \frac{2}{3}$ inches.

Compare your answer with the correct one above

Question

A regular hexagon has the same perimeter as the above right triangle. What is the length of one side of the hexagon?

Answer

By the Pythagorean Theorem, the hypotenuse of the right triangle is

$\sqrt{14^{2}+48^{2}} = \sqrt{196+2,304} = \sqrt{2,500} = 50$ inches, making its perimeter

inches.

The regular hexagon, which has six sides of equal length, has the same perimeter, so each side measures

$112 \div 6 = 18 \frac{2}{3}$ inches.

Compare your answer with the correct one above

Question

A regular hexagon has the same perimeter as the above right triangle. What is the length of one side of the hexagon?

Answer

By the Pythagorean Theorem, the hypotenuse of the right triangle is

$\sqrt{14^{2}+48^{2}} = \sqrt{196+2,304} = \sqrt{2,500} = 50$ inches, making its perimeter

inches.

The regular hexagon, which has six sides of equal length, has the same perimeter, so each side measures

$112 \div 6 = 18 \frac{2}{3}$ inches.

Compare your answer with the correct one above

Question

A regular hexagon has the same perimeter as the above right triangle. What is the length of one side of the hexagon?

Answer

By the Pythagorean Theorem, the hypotenuse of the right triangle is

$\sqrt{14^{2}+48^{2}} = \sqrt{196+2,304} = \sqrt{2,500} = 50$ inches, making its perimeter

inches.

The regular hexagon, which has six sides of equal length, has the same perimeter, so each side measures

$112 \div 6 = 18 \frac{2}{3}$ inches.

Compare your answer with the correct one above

Question

A regular hexagon has the same perimeter as the above right triangle. What is the length of one side of the hexagon?

Answer

By the Pythagorean Theorem, the hypotenuse of the right triangle is

$\sqrt{14^{2}+48^{2}} = \sqrt{196+2,304} = \sqrt{2,500} = 50$ inches, making its perimeter

inches.

The regular hexagon, which has six sides of equal length, has the same perimeter, so each side measures

$112 \div 6 = 18 \frac{2}{3}$ inches.

Compare your answer with the correct one above

Question

If the sum of angles in a hexagon is equal to $650^\circ$ , what is the value of the remaining sixth angle?

Answer

The sum of the angles in a polygon can be found using the equation below, in which t is equal to the total sum of the angles, and n is equal to the number of sides.

Given that a hexagon has 6 angles, the total number of angles will be:

$t=4\cdot 180$

Given that 5 of the angles have a sum of 650 degrees, we would subtract 650 from 720, resulting in 70 degrees.

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Question

If the sum of angles in a hexagon is equal to $650^\circ$ , what is the value of the remaining sixth angle?

Answer

The sum of the angles in a polygon can be found using the equation below, in which t is equal to the total sum of the angles, and n is equal to the number of sides.

Given that a hexagon has 6 angles, the total number of angles will be:

$t=4\cdot 180$

Given that 5 of the angles have a sum of 650 degrees, we would subtract 650 from 720, resulting in 70 degrees.

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Question

What is the sidelength, in feet and inches, of a regular hexagon with perimeter 16 feet?

Answer

Divide the perimeter 16 feet by 6 to get the sidelength of the hexagon in feet:

$16 \div 6 = 2\frac{2}{3} \textrm{ ft }$

Two-thirds of a foot is equal to eight inches, so this sidelength is 2 feet 8 inches.

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Question

The perimeter of a regular hexagon is one mile. Give the sidelength in feet.

Answer

One mile is equal to 5,280 feet, so divide this by 6:

$5,280 \div 6 = 880$ feet

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Question

The perimeter of a hexagon is 96cm. Find the length of one side.

Answer

A hexagon has 6 equal sides. To find the length of one side of a hexagon, we will use the formula to find the perimeter.

where a is the length of one side. So, we will solve for a.

Now, we know the perimeter of the hexagon is 96cm. So, we get

$96\text{cm} = 6a$

$\frac{96\text{cm}}{6} = \frac{6a}{6}$

$16\text{cm} = a$

$a = 16\text{cm}$

Therefore, the length of one side of the hexagon is 16cm.

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Question

A hexagon has a perimeter of 114in. Find the length of one side.

Answer

A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is:

where a is the length of any side. Now, to find the length of one side, we will solve for a.

We know the perimeter of the hexagon is 114in. So, we will substitute and solve for a. We get

$114\text{in} = 6a$

$\frac{114\text{in}}{6} = \frac{6a}{6}$

$19\text{in} = a$

$a = 19\text{in}$

Therefore, the length of one side of the hexagon is 19in.

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Question

Find the perimeter of a hexagon with one side having a length of 15cm.

Answer

To find the perimeter of a hexagon, we will use the following formula:

$P = 6 \cdot a$

where a is the length of one side of the hexagon.

Now, we know the length of one side of the hexagon is 15cm.

Knowing this, we can substitute into the formula. We get

$P = 6 \cdot 15\text{cm}$

$P = 90\text{cm}$

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Question

Find the perimeter of a hexagon with a side having a length of 13cm.

Answer

A hexagon has 6 sides. So, to find the perimeter, we will use the following formula:

where a is the length of one side.

Now, we know a side has a length of 13cm. Knowing this, we can substitute into the formula.

$P = 6 \cdot 13\text{cm}$

$P = 78\text{cm}$

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Question

A hexagon has a side of length 13cm. Find the perimeter.

Answer

To find the perimeter of a hexagon, we will use the following formula:

where a is the length of one side of the hexagon. We multiply it by 6 because a hexagon has 6 equal sides.

So, we know the length of one side is 13cm. Knowing this, we can substitute into the formula. We get

$P = 6 \cdot 13\text{in}$

$P = 78\text{in}$

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Question

Find the perimeter of a hexagon with a side having a length of 12in.

Answer

To find the perimeter of a hexagon, we will use the following formula:

$P = 6 \cdot a$

where a is the length of one side of the hexagon. Because a hexagon has 6 equal sides, we can use any side in the formula.

So, we know the length of one side is 12in. So, we can substitute. We get

$P = 6 \cdot 12\text{in}$

$P = 72\text{in}$

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