Atriangular pyramid with an equilateral base has a side length of 10 centimeters and a surface area of 214.5 square centimeters. find its slant height

Area of the lateral triangle is half or the product of the slant height and the side length. The slant height of the triangular pyramid is 11.143 centimetres.

Given information-

The side length of the triangular pyramid is 10 centimetres.

The surface area of the triangular pyramid is 214.5 square centimetres.

The slant height is the distance measured along a lateral face from the base to the top along the center of the pyramid.

The surface area of the equilateral triangular pyramid is the sum of the area of the base and three times the area of the lateral side.

Suppose the above equation as equation one.

Area of the base of the equilateral tangle can be given as,

The area of the lateral triangle is half or the product of the slant height and the side length. Thus,

Here l is the slant height of the triangle.

Keep the values in the equation 1,

Solve it for the l,

Thus the slant height of the triangular pyramid is 11.143 centimetres.

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hello from mrbilldoesmath!

answer:

a(n) - a(n-1) -3

discussion:

this ones a bit interesting. given a(n) = 5 - 3n consider this:

a(n-1) = 5 - 3(n-1)

          = (5 - 3n) + 3             => but a(n) = 5 - 3n, the first term

          = a(n)   + 3                 => subtract 3 from both sides

a(n-1) -3 = a(n)  

or

a(n) - a(n-1) -3

you,

mrb

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

step-by-step explanation: