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.
7 answers
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 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.
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.
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
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.
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.
3 answers