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Morgarella [4.7K]
2 years ago
15

Help me please :) thanks

Mathematics
1 answer:
Nata [24]2 years ago
3 0

The area of a 2D form is the amount of space within its perimeter. The lateral area of the triangular prism is 724.28m², while the total area of the prism is 752.28m². The surface area of the cylinder will be 414 in².

<h3>What is an area?</h3>

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

A.) The area of the lateral faces are:

Latera area of the triangular prism = (38×7)+(38×8.06)+(38×4) = 724.28m²

The total area of the prism is:

The total area of the prism = Lateral Area + Area of the base face

                                              = 724.28m² + 2(0.5×7×4)

                                              = 724.28m² + 28m²

                                              = 752.28m²

Hence, the lateral area of the triangular prism is 724.28m², while the total area of the prism is 752.28m².

B.) The surface area of the cylinder can be written as,

Surface Area = 2πrl + 2πr²

                      = (2×π×9×14) + (2×π×9×9)

                      = 252in² + 162in² = 414in²

Hence, the surface area of the cylinder will be 414 in².

Learn more about Area:

brainly.com/question/1631786

#SPJ1

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<h3>Answer:  A.  18*sqrt(3)</h3>

=============================================

Explanation:

We'll need the tangent rule

tan(angle) = opposite/adjacent

tan(R) = TH/HR

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54*sqrt(3)/3 = TH .... multiply both sides by 54

(54/3)*sqrt(3) = TH

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TH = 18*sqrt(3) which points to <u>choice A</u> as the final answer

----------------------

An alternative method:

Triangle THR is a 30-60-90 triangle.

Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.

The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.

Now use the pythagorean theorem

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(TH)^2 + (HR)^2 = (TR)^2

(x)^2 + (54)^2 = (2x)^2

x^2 + 2916 = 4x^2

2916 = 4x^2 - x^2

3x^2 = 2916

x^2 = 2916/3

x^2 = 972

x = sqrt(972)

x = sqrt(324*3)

x = sqrt(324)*sqrt(3)

x = 18*sqrt(3) which is the length of TH.

A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.

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