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Lana71 [14]
3 years ago
9

Hello! How do I find the surface area of this prism? Thanks!

Mathematics
1 answer:
Studentka2010 [4]3 years ago
8 0
Answer: Choice C) 124 square cm

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

Explanation:

Let's calculate the area of the trapezoid shown
b1 and b2 are the parallel bases; h is the height of the 2D trapezoid
b1 = 2
b2 = 5
h = 1.5

A = h*(b1+b2)/2
A = 1.5*(2+5)/2
A = 1.5*7/2
A = 10.5/2
A = 5.25
The area of one 2D trapezoid is 5.25 sq cm
There are two of these trapezoids that form the base faces of the trapezoidal prism. So the total base area is 2*5.25 = 10.5 sq cm
Keep this value (10.5) in mind. We'll use it later.

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

Now onto the lateral surface area (LSA)
It turns out that the formula for the LSA is
LSA = p*d
where 
p = perimeter of the trapezoid shown
d = depth or height of the 3D trapezoid (I'm not using h as it was used earlier)
This formula works for any polygonal base. It doesn't have to be a trapezoid.

In this case the perimeter is,
p = 1.7+2+2.65+5
p = 11.35

So
LSA = p*d
LSA = 11.35*10
LSA = 113.5

Add this LSA to the base area found earlier
10.5+113.5 = 124

The total surface area is 124 square cm
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E
xz_007 [3.2K]

Answer:

1) n = 84

2) n = 78

3) n = 24

4) n = 16

5) n = 35

Step-by-step explanation:

To solve each proportion, we apply cross multiplication.

Question 1:

\frac{5}{12} = \frac{35}{n}

5n = 35*12

Simplifying both sides by 5

n = 7*12 = 84

Question 2:

\frac{n}{52} = \frac{180}{120}

120n = 52*180

Simplifying both sides by 20

6n = 52*9

Simplifying by 3

2n = 52*3

Simplifying by 2

n = 26*3 = 78

Question 3:

\frac{18}{n} = \frac{21}{28}

21n = 18*28

Simplifying both sides by 7

3n = 18*4

Simplifying both sides by 3

n = 6*4 = 24

Question 4:

\frac{n}{4} = \frac{24}{6}

\frac{n}{4} = 4

n = 16

Question 5:

\frac{10}{16} = \frac{n}{56}

16n = 56*10

Simplifying by 2, both sides

8n = 56*5

Simplifying by 8, both sides

n = 7*5 = 35

4 0
3 years ago
What is the correct value for the expression below? 2−1+50
Akimi4 [234]

Answer:

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Step-by-step explanation:

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3 years ago
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Answer:

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Step-by-step explanation:

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3 years ago
Which equation will have the same solution as 3 – 5(2x + 1) = 3(3 + x)?A.
Nonamiya [84]
The answer is C
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3 years ago
What is the volume of the triangular prism <br><br> A) 12 cm<br> B) 18<br> C) 24<br> D) 48
lisov135 [29]

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2 years ago
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