3 years ago

I need help with number 3

1 answer:

6 0

The hexagon divides the circle into 6 parts. That means the angle projecting each side is: 360°÷ 6 = 60°

The area of a circle is: πr²
78.54 in² divided by pi is 25 making the radius = 5

I would then use SOH CAH TOA to solve for the side.. knowing the hypotenuse is the radius and the angle to split it into a right triangle is 30°

Sin(30) = s/5
5*Sin(30) = s

12*s = perimeter hexagon
(remember s is half the hexagon side)

12*5*Sin(30) = perimeter hexagon
30 inches = perimeter

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Full steps and all reasons, thanks!

Nataly_w [17]

You can focus on the two sub-triangles ABC and ACD

We know that they are both right triangles, because we're given that AC and BD are perpendicular.

The sides AB and AD are the hypothenuses of these triangles, so we know their length through the pythagorean theorem:

$AD^2 = AC^2+CD^2$

$AB^2 = AC^2+BC^2$

But since we're given $BC=CD$ , the expressions for AD and AB are actually the same expression. This proves that AD=AB, and thus that the triangle is isosceles.