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suter [353]
4 years ago
13

What is the approximate area of a regular pentagon with a side length of 6 feet and a distance from the center to a vertex of 6

feet?
Mathematics
2 answers:
Sergio [31]4 years ago
6 0
The answer is 7,776.
Sedbober [7]4 years ago
6 0
In order to find the area of a regular Pentagon, which is composed of 5 congruent isosceles triangles with bases (b) being the sides of the Pentagon (P).
So b = 6ft.
Distance from the center, where all 5 triangle apexes touch, to each vertex also makes the sides of the triangles. This = 6ft. We'll call it side (s). Now to find the area of each triangle, we need the apothem, which is the height of the Isosceles triangle. The height (h) or apothem bisects the polygon side/triangle base (b) into 2 equal lengths. So b/2 = 6/2 = 3ft.
Now we have 2 right triangles making up each of the 5 triangles, split by the apothem h.
We can find h by Pythagorean Theorem: h^2 = (b/2)^2 + s^2
So h^2 = 3^2 + 6^2 = 9 + 36 = 45
So square root (sr) of h^2 = h, which = square root of 45
--> h = sr (9) × sr (5) = 3sr5
Now the area of a triangle (At) = 1/2 b×h --> At = 3×3sr5 = 9sr5
Now that's one triangle, multiply it by 5 to get the area of all 5 triangles, which as we've said make up the Area of the regular Pentagon (P).
So P = 5 × 9sr5 = 45sr5, or approximately 100.62 ft. squared
Hope this helps!
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gavmur [86]

Answer:

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Step-by-step explanation:

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4 0
3 years ago
if you divide a positive number by 12, the answer would be less than the original number? always, sometimes, or never​
elena55 [62]

Answer:

Always

Step-by-step explanation:

The rules for positive numbers is that addition and multiplication makes numbers larger. Subtraction and division makes numbers smaller.

Since 12 is a positive number, the result of dividing a positive number by 12 will make it smaller.

8 0
4 years ago
Can someone help me with this : 4g = 8
ratelena [41]

Answer:

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Your answer would be

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7 0
3 years ago
Read 2 more answers
Mason can walk 4 miles in 1 hour.how many miles can he walk in 3 hours
sdas [7]
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3 0
3 years ago
Is (-2, -6) a solution to this system of equations? 3x + 18y = -14 15x − 7y = 12 yes no
soldi70 [24.7K]

Answer:

No

Step-by-step explanation:

Plug in (-2, -6) to see if it's the solution or not

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Answer is NO

6 0
4 years ago
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