Find the area of the regular polygon round to the nearest tenth
2 answers:
Answer:
The area of this polygon is 98.1 yd²
Step-by-step explanation:
<em>Check the image below</em>.
The diagonal line from the corner of a square to the center of this one will shape an isosceles triangle.
The Pythagoras theorem give us the following formula:
A² + A² = H²
Both "A" are the sides and H is the hypotenuse, seeing the figure, the diagonal coincide with the hypotenuse and the measure is 7 yd.
A² + A² = 72
2A² = 49
A²= 49/2
A²= 24. 5
A=√24.5
A= 4.95 yd
Knowing that the diagonal ends up in the center of the square, we assume that the side of the triangle (“A” side) is the half of the side of the square, then this last one is 2A. Bearing in mind that square have all of the sides with the same measure, the four sides have a 2A size.
2A = 2(4.95) =9.9 yd
Each side of the square measures 9.9 yd
The area of a square is
Side²= (2A)2²
(9.9)²= 98.1 yd²
The area of this polygon is 98.1 yd²
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Answer:
a) h = 123/x^2
b) S = x^2 +492/x
c) x ≈ 6.27
d) S'' = 6; area is a minimum (Y)
e) Amin ≈ 117.78 m²
Step-by-step explanation:
a) The volume is given by ...
V = Bh
where B is the area of the base, x^2, and h is the height. Filling in the given volume, and solving for the height, we get:
123 = x^2·h
h = 123/x^2
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b) The surface area is the sum of the area of the base (x^2) and the lateral area, which is the product of the height and the perimeter of the base.
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c) The derivative of the area with respect to x is ...
When this is zero, area is at an extreme.
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d) The second derivative is ...
This is positive, so the value of x found represents a minimum of the area function.
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e) The minimum area is ...
The minimum area of metal used is about 117.78 m².