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Svetlanka [38]
3 years ago
15

Please help me i really need help please

Mathematics
1 answer:
Svetllana [295]3 years ago
7 0

Answer:

option 1

Step-by-step explanation:

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Find the area of an octagon with a radius of 6 meters
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A regular octagon has all its eight sides congruent. The line segments joining each of the vertices of a regular octagon to its center are called the radii of the octagon. These 8 radii divide a regular octagon into 8 congruent isosceles triangles. Area of each isosceles triangle is

A_{triangle}=\dfrac{1}{2}a^2\sin \alpha,

where a is length of the side of the octagon and \alpha is the angle between two radii of the octagon.

In regular octagon

\alpha=\dfrac{360^{\circ}}{8}=45^{\circ}.

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A_{octagon}=8A_{triangle}=8\cdot \dfrac{1}{2}a^2\sin \alpha=4\cdot (6)^2\cdot \sin 45^{\circ}=4\cdot 36\cdot \dfrac{\sqrt{2}}{2}=72\sqrt{2} sq. m.

Answer: A_{octagon}=72\sqrt{2} sq. m.


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