A nut is shaped like a regular hexagon with side lengths of 1 centimeter. Find the value of x .
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Answer:
x = √3
A complete question related to this found on chegg is stated below:
A nut is shaped like a regular hexagon with side lengths of 1 centimeter. Find the value of x . (Hint: A regular hexagon can be divided into six congruent triangles.)
Find attached the diagram.
Step-by-step explanation:
Side length = 1cm
A regular hexagon has six equal the side length. A line drawn from the center to any vertex will have the same length as any side.
This implies the radius is equal to the side length.
As a result, when lines are drawn from the center to each of the vertex, a
regular hexagon is said to be made of six equilateral triangles.
From the diagram, x = 2× apothem
Apothem is the distance from the center of a regular polygon to the midpoint of a side.
Using Pythagoras theorem, we would get the apothem
Hypotenuse ² = opposite ² + adjacent²
1² = apothem² + (½)²
Apothem = √(1² -(½)²)
= √(1-¼) = √¾
Apothem = ½√3
x = 2× Apothem = 2 × ½√3
x = √3
x = √3
A complete question related to this found on chegg is stated below:
A nut is shaped like a regular hexagon with side lengths of 1 centimeter. Find the value of x . (Hint: A regular hexagon can be divided into six congruent triangles.)
Find attached the diagram.
Step-by-step explanation:
Side length = 1cm
A regular hexagon has six equal the side length. A line drawn from the center to any vertex will have the same length as any side.
This implies the radius is equal to the side length.
As a result, when lines are drawn from the center to each of the vertex, a
regular hexagon is said to be made of six equilateral triangles.
From the diagram, x = 2× apothem
Apothem is the distance from the center of a regular polygon to the midpoint of a side.
Using Pythagoras theorem, we would get the apothem
Hypotenuse ² = opposite ² + adjacent²
1² = apothem² + (½)²
Apothem = √(1² -(½)²)
= √(1-¼) = √¾
Apothem = ½√3
x = 2× Apothem = 2 × ½√3
x = √3
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