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DiKsa [7]
3 years ago
5

You have 100 yards of fencing available to create an enclosure for farm animals. As the

Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
3 0
1. area of a pentagon when 1 side is x is \frac{x^2}{4}\sqrt{5(5+2\sqrt{5})}
so if perimiter is 100 then one side is 100/5 or 20
area will be \frac{20^2}{4}\sqrt{5(5+2\sqrt{5})}≈<span>688.2 square yards

2. area of a hexagon when 1 side is length x is \frac{3x^2\sqrt{3}}{2}
so if permiter is 100 then length of one side is 100/6 or about 16.666666666666
the area will be \frac{3(16.6666666)^2\sqrt{3}}{2}≈721.7 square yards

3. area of a regular octagon with side lenghts x is 2(1+\sqrt{2})x^2
so if 8 sides then side length of each is 100/8 or 12.5
area will be 2(1+\sqrt{2})12.5^2≈754.4 square yards


octagon wil have most space
you can tell because the more sides it has, the more it gets to a circle and the more area it encloses with a given perimiter
</span>
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2\%2%2, percent of the students at Hamilton Middle School have red hair. There are 700700700 students at Hamilton Middle School.
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<u>14 students</u> at Hamilton Middle School have red hair.

Step-by-step explanation:

Given:

2%, percent of the students at Hamilton Middle School have red hair.

There are 700 students at Hamilton Middle School.

Now, to find the number of students at Hamilton Middle School having red hair.

Total number of students = 700.

Percent of the students at Hamilton Middle School have red hair = 2%.

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Answer:

1. S.A. = 4350 cm²

2. S.A. = 864 cm²

3. S.A. = 240 cm²

4. S.A. = 224 m²

5. S.A. = 301.6 in.²

6. S.A. = 6,082.1 cm²

7. S.A. = 923.6 in.²

Step-by-step explanation:

1. Surface area of the rectangular prism = 2(LW + LH + WH)

L = 45 cm

W = 25 cm

H = 15 cm

S.A. = 2(45*25 + 45*15 + 25*15)

S.A. = 4350 m²

2. Surface area of the cube = 6a²

a = 12 cm

S.A. = 6(12²)

S.A. = 864 cm²

3. Surface area of triangular prism = bh + (s1 + s2 + s3)*H

b = 4 cm

h = 6 cm

s1 = 4 cm

s2 = 7 cm

s3 = 7 cm

H = 12 cm

Plug in the values

S.A. = 4*6 + (4 + 7 + 7)*12

S.A. = 24 + (18)*12

S.A. = 24 + 216

S.A. = 240 cm²

4. Surface area of the square based pyramid = area of the square base + 4(area of 1 triangular face)

S.A. = (8*8) + 4[(8*10)/2]

S.A. = 64 + 4(40)

S.A. = 64 + 160

S.A. = 224 cm²

5. Surface area of the cone = πrl + πr²

r = 6 in.

l = 10 in.

S.A. = π*6*10 + π*r²

S.A. = 60π + 36π

S.A. = 301.592895

S.A. = 301.6 in.² (nearest tenth)

6. Surface area of the sphere = 4πr²

r = 22 cm

S.A. = 4*π*22²

S.A. = 1,936π

S.A. = 6,082.1 cm² (nearest tenth)

7. Surface area of the cylinder = 2πrh + 2πr²

r = 7 in.

h = 14 in.

S.A. = 2*π*7*14 + 2*π*7²

S.A. = 923.6 in.² (nearest tenth)

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