mathh helpp?

Question

The base of a triangular prism is an equilateral triangle with a perimeter of 42 cm. If the height of the prism is 10 cm, what is the lateral area?

Answer 1

to get the lateral area of a prism (surface area of all faces except the bases) you multiply the perimeter of the base by the height of the object
so 42*10 = 420sq. cm.

this works because all of the faces in a prism that count toward the lateral area are rectangular

lets take a triangular prism for example where the side lengths of the base are x, y, and z and the height of the prism is H
you will have 3 rectangles whose areas are xH yH and zH
you can then write the total lateral area as
xH+yH+zH
which you can factor to
H(x+y+z)
and x+y+z is also known as:
H(perimeter of the base)

Answer 2

One side of the base, s = perimeter/3 = 42/3 =14 cm - all the sides are equal.

Now you have a line from one corner of the base to the height of the prim in the plane of the base and another line from the height of the prism to the middle of one side of the base in the lpane of the base. The is latter line is a segment of the bisecotr of the angle opposite base line you picked which also bisects teh baseline.

So in the plane of the base we have a right triangle with a 30 degree angle where the hypotoneus comes from the corner to the height of the prism. and a side of length s/2. The hypotoneus has a length

h = s/2/cos(30) = 7/cos(30) = 14/sqrt(3)

Now perpendicular to the plae of the base, the hypotoneus we just found forms on side of a right triangle with the height as the other side. So the slant height is:

Sl = sqrt(h^2 + 10^2) = sqrt(14^2/3+100) = 12.86 cm

so there are three isocoles triangles with two sides of 12.86 cm and one side of 14 cm.

Now each triangle has Area = A = 1/2* base*height

Height = sqrt(12.86^2+(14/2)^2) = 14.64 cb

so Area = 1/2*14*14.64 = 102.5 cm^2

And total area = 3*area = 307.5 cm^2

Answer 3

You just multiply Perimeter x height = 420

check this:
http://www.kwiznet.com/p/takeQuiz.php?ChapterID=11213&CurriculumID=48

Answer 4

# Write the equation of the line in slope-intercept type that's PARALLEL to the line 4x + y = 6 and has a y-intercept of 8. y= -4x +8 what's the equation of the line in slope-intercept type (y=mx+b) that is going contained in the direction of the element (4, 5) and is PERPENDICULAR to y= -a million/2x+7? y= a million/2x+3 what's the equation of the line that is going contained in the direction of the element (5, a million) and has UNDEFINED slope x=5 Write the equation of the line whose slope is UNDEFINED and is going contained in the direction of the element (a million, 3). x=a million Write the equation of the line that passes contained in the direction of the element (-4, -3) and has a slope of 0. y=-3 # what's the equation of the line that's parallel to the x axis and is going contained in the direction of the element (-4, -2)? y=-2