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AJoey used 10 congruent triangles to create a regular decagon.

What kind of triangles is he using?


b)Joey used 10 congruent triangles to create a regular decagon.


Find the three angle measures of one of the triangles. Explain how you know.


c)Joey used 10 congruent triangles to create a regular decagon.


If the area of each triangle is 14.5 square inches, then what is the area of the regular decagon? Show all work.

Verified Answer :

Edufirst

A) Joey used 10 congruent triangles to create a regular decagon.


What kind of triangles is he using?

He is using isosceles triangles. because the two sides (of each triangle) whose vertix is at the center of the decagon are congruent, while the third side, is different.

b)Joey used 10 congruent triangles to create a regular decagon.


Find the three angle measures of one of the triangles. Explain how you know.

The angle between the two congruent sides is equal to 360° divided by the number of triangles.

360° / 10 = 36.

The other two angles are congruent and must obey the rule of 180°.

2x + 36 = 180 => 2x = 180 - 36 = 144

x = 144 / 2 = 72°

Then two angles are 72° and the other is 36°.

c)Joey used 10 congruent triangles to create a regular decagon.


If the area of each triangle is 14.5 square inches, then what is the area of the regular decagon? Show all work.

The area of the decagon is ten times the area of a triangle.

Area of the decagon = 10 * 14.5 in^2 =  145 in^2.


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