Answer:
Step-by-step explanation:
Left Frame
<u>Formula</u>
Area of Hexagon = 3*sqrt(3)*a^2 / 2
Area of a Square = a^2
In both cases a is a side length
<u>Givens</u>
A = 384*sqrt(3)
<u>Solution</u>
384*sqrt(3) = 3*sqrt(3)*a^2 / 2 Divide by sqrt(3) on both sides.
384 = 3 * a^2 / 2 Multiply by 2
768 = 3 * a^2 Divide by 3
256 = a^2 Take the square root of both sides
a = 16
Each side of the square will be = a
The area of the square = a^2
a^2 = 16^2 = 256
Center Frame
I don't know how to expand the question so that I'm doing some sort of step-by-step explanation. The question just means what does a equal when t = 0
The answer is 15.
Right Frame
The tangents meet the circumference of the circle at a 90o angle when the radius is connected by the point of contact. Call the central angle (LON) = x
The two tangents and the two radii form a kite which is a quadrilateral.
All quadrilaterals have 4 angles that add up to 360.
x + 90 + 90 + 60 = 360 Combine the like terms on the left
x + 240 = 360 Subtract 240 from both sides
x = 360 - 240
x = 120
The length of the arc is given by (Central angle / 360) * Circumference
x is the central angle so the central angle = 120
Length = (120 / 360) * 96
Length = 1/3 * 96
Length = 32
