Answer :
The area of a regular hexagon is a. [tex]{585 \text{ in}^2}[/tex].
To find the area of a regular hexagon, we can use the formula [tex]\( A = \frac{3\sqrt{3}}{2} \cdot a^2 \)[/tex], where a is the length of one side of the hexagon.
Given that the side of the hexagon is 15 inches long, we can substitute this value into the formula:
[tex]\( A = \frac{3\sqrt{3}}{2} \cdot (15 \text{ in})^2 \)\\\\\\ \( A = \frac{3\sqrt{3}}{2} \cdot 225 \text{ in}^2 \)\\\\ \( A = \frac{3\sqrt{3}}{2} \cdot 225 \text{ in}^2 \)\\ \\\( A = \frac{3 \cdot 225 \cdot \sqrt{3}}{2} \text{ in}^2 \)\\ \\\( A = \frac{675 \cdot \sqrt{3}}{2} \text{ in}^2 \)\\ \\\( A \approx \frac{675 \cdot 1.732}{2} \text{ in}^2 \)\\ \\\( A \approx \frac{1169.1}{2} \text{ in}^2 \)\\ \\\( A \approx 584.55 \text{ in}^2 \)[/tex]
Rounding to the nearest tenth, we get:
[tex]\( A \approx 585 \text{ in}^2 \)[/tex]
Therefore, the area of the regular hexagon is approximately [tex]\( 585 \text{ in}^2 \)[/tex].
The complete question is- Find the area of a regular hexagon with an apothem 13 inches long and a side 15 inches long. Round your answer to the nearest tenth.
a. 585 in²
b. 389.7 in²
c. 97.4 in²
d. 1,169.1 in²
Answer:
Option 1st is correct
585 [tex]\text{in}^2[/tex]
Step-by-step explanation:
Area(A) of a regular hexagon is given by:
[tex]A = \frac{1}{2}P \cdot a[/tex] ....[1]
where,
P is the perimeter and a is the apothem of the regular hexagon.
As per the statement:
An apothem 13 inches long and a side 15 inches long.
⇒a = 13 inches and side = 15 inches
Perimeter of hexagon(P) = 6s ; where s is the side
⇒P = 6(15) = 90 inches
Substitute the given values in [1] we have;
[tex]A = \frac{1}{2} \cdot 90 \cdot 13[/tex]
Simplify:
A = 585 square inches.
Therefore, the area of a regular hexagon with an apothem 13 inches long and a side 15 inches long is, [tex]585 in^2[/tex]
