What is the area of a regular hexagon with an apothem 13 inches long and a side 15 inches long? Round the answer to the nearest inch.
The formula for the area of a regular hexagon is:
Area = (3 × √3 × apothem2) ÷ 2
We're given that the apothem is 13 inches long, so we can substitute that into the formula:
Area = (3 × √3 × 132) ÷ 2
Area = (3 × √3 × 169) ÷ 2
Area = (507√3) ÷ 2
Area = 253.5√3
Now we need to round to the nearest inch. To do this, we'll use the following method:
- Multiply the decimal portion of the answer by √3 (which is about 1.732) to get the decimal portion of the answer in inches.
- Round that decimal to the nearest inch.
- Add that rounded value to the whole number of the answer to get the final answer rounded to the nearest inch.
So:
- 0.5 × 1.732 = 0.866
- Rounded to the nearest inch, 0.866 is 1.
- 253 + 1 = 254
Therefore, the area of the regular hexagon is approximately 254 square inches.
What is the area of a regular hexagon with an apothem 13 inches long and a side 15 inches long? Round the answer to the nearest inch.
the options are
585 in^2
390 in^2
97 in^2
1,169 in^2
The correct answer is 585 in².
The area of a regular hexagon with an apothem a and a side s is given by the formula:
Area = (3 × √3 × a²) ÷ 2
We're given that the apothem is 13 inches long and the side is 15 inches long.
Using the formula, we can calculate the area as:
Area = (3 × √3 × 13²) ÷ 2
Area = (3 × √3 × 169) ÷ 2
Area = (507√3) ÷ 2
Area ≈ 585
Rounding to the nearest inch, we get:
Area ≈ 585 in²
Therefore, the correct option is 585 in².
what is the area of a regular hexagon with an apothem 20.5 inches long and a side 23 inches long round the answer to the nearest tenth
The area of this hexagon can be calculated using the formula:
Area = (3 × √3 × apothem²) ÷ 2
Substituting the given values:
Area = (3 × √3 × 20.5²) ÷ 2
Area ≈ 3224.72
Rounding to the nearest tenth:
Area ≈ 3224.7
Therefore, the area of the regular hexagon is approximately 3224.7 square inches.
what is the area of a regular hexagon with an apothem 20.5 inches long and a side 23 inches long round the answer to the nearest tenth
A. 1886.0
B. 2829.0
C. 235.8
D. 1,414.5
The correct formula to calculate the area of a regular hexagon with an apothem is:
Area = (3 × √3 × apothem²) ÷ 2
Substituting the given apothem length:
Area = (3 × √3 × 20.5²) ÷ 2
Area ≈ 3224.72
Rounding to the nearest tenth:
Area ≈ 3224.7
Therefore, the correct answer is not among the options given.