Question

Help with these two, never was taught how to be taught to solve these.

Answer 1

The area of the given regular hexagon with sides measuring 110 units and an apothem of 62 units is approximately 5238.3 square units, and its perimeter is 660 units.

To calculate the area of a regular hexagon, we can use the formula:

`\[ A = (s^2 * √(3))/(4) \]`

where \( s \) is the length of a side.

For the given hexagon with sides measuring 110 units:

`\[ A = ((110)^2 * √(3))/(4) \]`

`\[ A = (12100 * √(3))/(4) \]`

`\[ A \approx (12100 * 1.732)/(4) \]`

`\[ A \approx (20953.2)/(4) \]`

`\[ A \approx 5238.3 \, \text{square units} \]`

Therefore, the area of the regular hexagon is approximately 5238.3 square units.

To calculate the perimeter of the hexagon, we use the formula:

`\[ \text{Perimeter} = \text{Number of sides} * \text{Length of a side} \]`

For the given hexagon with sides measuring 110 units:

`\[ \text{Perimeter} = 6 * 110 \]`

`\[ \text{Perimeter} = 660 \, \text{units} \]`

Therefore, the perimeter of the regular hexagon is 660 units.

The probable question may be:

Given a regular hexagon with sides measuring 110 units each and an apothem of 62 units, what is the area of the hexagon? Additionally, what is the perimeter of the hexagon?