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Andreyy89
3 years ago
13

Find the lateral area the regular pyramid.

Mathematics
2 answers:
Leto [7]3 years ago
8 0

Answer:

<h3>The lateral area of the pyramid is 180 unit².</h3>

Step-by-step explanation:

We are given a hexagonal pyramid with dimensions,

Base (B)= 6 units and Height (H) = 8 units

Now, the lateral area of the pyramid = \frac{1}{2}PL, where P = perimeter of the base and L = slant height.

Since, the base of the pyramid is a hexagon.

So, the perimeter of an hexagon = 6\times Side = 6 × 6 = 36 units

Also, the slant height is given by,

L^{2}=\sqrt{B^{2}+H^{2}}\\\\L^{2}=\sqrt{6^{2}+8^{2}}\\\\L^{2}=\sqrt{36+64}\\\\L^{2}=\sqrt{100}\\\\L=\pm 10

Since, the slant height cannot be negative. So, L = 10 units.

Substituting the values gives,

The lateral area of the pyramid = \frac{1}{2}\times 36\times 10=36\times 5=180

<h3>Thus, the lateral area of the pyramid is 180 unit².</h3>
vladimir2022 [97]3 years ago
4 0

Answer:

180

Step-by-step explanation:

The general formula for the lateral surface area of a regular pyramid is

L.S.A = 1/2 (p)(l)

where p represents the perimeter of the base and l the slant height

Slant height

The hexagon can be broken down into 6 equilateral triangles.  Each side of the equilateral triangle is equal, therefore, the diagonal is twice the side length of the hexagon and the distance from one vertex to mid is half the diagonal.

By considering a right triangle at the centre, we will apply pythagorus theorem

Hypotenuse² = base² + height²

slantHeight² = 6² + 8²

slantHeight = √(6²+8²)

                   = 10

Perimeter of base

6(6) = 36

L.S.A = 1/2 (36)(10)

         = 180

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4 0
3 years ago
How many feet long is the shadow of a 15-foot flagpole if a 5-foot woman standing at the base of the flagpole has a shadow that
Vikentia [17]

The height of flagpole is 12.5 feet.

Step-by-step explanation:

Given,

Height of woman = 5 foot

Shadow of woman = 6 feet

Ratio of height to shadow = 5:6

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Height of flagpole = x

Ratio of height to shadow = x:15

Using proportion;

Ratio of height to shadow :: Ratio of height to shadow

5:6::x:15\\

Product of mean = Product of extreme

6*x=15*5\\6x=75

Dividing both sides by 6

\frac{6x}{6}=\frac{75}{6}\\x=12.5

The height of flagpole is 12.5 feet.

Keywords: ratio, proportion

Learn more about proportion at:

  • brainly.com/question/9527422
  • brainly.com/question/9381523

#LearnwithBrainly

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3 years ago
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qwelly [4]

Answer:

2/4 1/2 5/10 6/12 10/20

Step-by-step explanation:

just pick an even denominator and take half of that number for the numerator. This only works because the most basic form of 4/8 is 1/2. This method only works if your selected fraction is equivalent to 1/2.

7 0
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The answer is probably C or D
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