Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
5. Solving Square Root and Other Radical Equations
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Exercise 45 Page 395

Looking at the diagram, we see that the height of the triangle at the bottom is and one side of it is For the hexagon to be regular, the triangles must all be equilateral and, therefore, congruent. Let's first show that the triangle at the bottom is indeed an equilateral triangle.

The measure of the interior angle of a regular hexagon must be We see that the angles are bisected by triangles so all triangles have two angles. The Interior Angles Theorem tells us that the triangles must be equilateral then because

Each triangle is an equilateral triangle with a side of Area of an equilateral triangle with a side of can be expressed as below.
Since the hexagon consists of six equilateral triangles, we can find the area of the hexagon by multiplying by six.
Therefore, the formula for the area of the hexagon is We know the area of the hexagon, let's find the length of one side of the hexagon using the formula we found above.
Solve for
Upon reaching this state, we will need to find the square root of both sides of the equation in order to isolate further.
Solve for
The length of each side of the hexagon is about