To use the area formula for triangles, we need to divide the hexagon into six congruent triangles. Draw lines from the center of the hexagon to each vertex, dividing the hexagon into six congruent equilateral triangles.
Each of these triangles has a base of 10 and a height of $\frac{10\sqrt{3}}{2}=5\sqrt{3}$. Therefore, the area of each triangle is $\frac{1}{2}(10)(5\sqrt{3})=25\sqrt{3}$.
Since there are six congruent triangles in the hexagon, the total area of the hexagon is $6(25\sqrt{3})=\boxed{150\sqrt{3}}$.
Find the area of the regular hexagon below by using the area formula for triangles.
3 answers
that makes no sense just use / and ^
We can use the formula for the area of a regular hexagon, which is:
$A=\frac{3\sqrt{3}}{2}s^2$
where $s$ is the length of one side of the hexagon.
Since all sides of a regular hexagon are congruent, we can let $s=10$ (given in the diagram), and substitute into the formula:
$A=\frac{3\sqrt{3}}{2}(10)^2$
Simplifying:
$A=\frac{3\sqrt{3}}{2}(100)$
$A=150\sqrt{3}$
Therefore, the area of the regular hexagon is $\boxed{150\sqrt{3}}$.
$A=\frac{3\sqrt{3}}{2}s^2$
where $s$ is the length of one side of the hexagon.
Since all sides of a regular hexagon are congruent, we can let $s=10$ (given in the diagram), and substitute into the formula:
$A=\frac{3\sqrt{3}}{2}(10)^2$
Simplifying:
$A=\frac{3\sqrt{3}}{2}(100)$
$A=150\sqrt{3}$
Therefore, the area of the regular hexagon is $\boxed{150\sqrt{3}}$.