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# Help me with math plz!!

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Question #1

Question #2

Question #3

Question #4

Question #5

Apr 27, 2018

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First one :

The slant height, h,  is  given by :

sin 60  = h / 8     multiply both sides by  8

8 * sin 60  =  h

8 * √3 / 2  = h

4√3 m  = h

Second one

The base area  is composed of 6 equilateral triangles.......

The total area  is  given  by :  6 (1/2) (14) (14) sin (60°)  =   3 * 196 *  √3/ 2   = 294√3 cm^2

Third one ;

The base area is a square with a side of 6 ft....so its area  = 6^2  = 36 ft^2

The sides are triangles  with   bases of 6 and heights of 3....and we have 4 of them....so their area  is just :

4 * (1/2) (6) * 3  =   36  ft^2

So the surface area  = [ 36 + 36 ] ft^2  = 72 ft^2

Fourth one :

The base is a square with a side  of 6.2 yd....so its area  is  (6.2)^2  =  38.44 yd^2

The sides are 4 equal area triangles.....their bases are 6.2 yds

Their heights, h,  can be found as   tan(60)  = h / (6.2 * (1/2) )

√3  =  h / 3.1       multiply both sides by 3.1

3.1 * √3   = h

So the area of each triangle  = (1/2) base) (height)  = (1/2) (6.2) * 3.1 * √3   ≈ 16.645 yd^2

And we need to multiply ths by 4  =  66.58 yd^2

So...the total surface area  is   [  38.44 + 66.58  ] yds^2  ≈  105 yds^2

Last one ;

We have  8  equal area triangles comprising the lateral surface area .......we can find the height of each triangle as the hypotenuse of a right triangle with legs of 8.......this height  is :  √ [ 8^2 + 8^2 ]  = 8√2 cm

So....the total lateral surface  area  is

8 * (1/2) base of each triangle * its  height   =

8 * (1/2) * 6.6 * 8√2   =

4 * 6.6 * 8√2  =  298.7 cm^2

Apr 27, 2018