Answer:
(B) 123.2 yd²
Explanation:
You want the area of the decagon shown with side length 4 yd and apothem 6.16 yd.
Area
The area is given by the formula ...
A = 1/2Pa
where P is the perimeter and 'a' is the apothem, the distance from the center to the middle of one side of the regular polygon.
Application
The perimeter is the sum of the side lengths. Each of the 10 sides has a length of 4 yd, so that sum is 10·4 yd = 40 yd.
Using the known values in the formula, we find the area to be ...
A = 1/2(40 yd)(6.16 yd)
A = 123.2 yd²
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Additional comment
Effectively, you are computing 10 times the area of the triangle that is the area of one sector. That triangle has a base of 4 yd and a height of 6.16 yd. Its area is ...
A = 1/2bh = 1/2(4 yd)(6.16 yd) = 12.32 yd²
The 10 sectors of the decagon will have an area of ...
A = 10 × 12.32 yd² = 123.2 yd²