1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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
You might be interested in
2/x + 3/y = 13 ; 5/x - 4/y = -2​
Tomtit [17]

Given that

(2/x)+(3/y) = 13--------(1)

(5/x)-(4/y) = -2 -------(2)

Put 1/x = a and 1/y = b then

2a + 3b = 13 ----------(3)

On multiplying with 5 then

10a +15 b = 65 -------(4)

and

5a -4b= -2 ----------(5)

On multiplying with 2 then

10 a - 8b = -4 -------(6)

On Subtracting (6) from (4) then

10a + 15b = 65

10a - 8b = -4

(-)

_____________

0 + 23 b = 69

______________

⇛ 23b = 69

⇛ b = 69/23

⇛ b =3

On Substituting the value of b in (5)

5a -4b= -2

⇛ 5a -4(3) = -2

⇛ 5a -12 = -2

⇛ 5a = -2+12

⇛ 5a = 10

⇛ a = 10/5

⇛ a = 2

Now we have

a = 2

⇛1/x = 2

⇛ x = 1/2

and

b = 3

⇛1/y = 3

⇛ y = 1/3

<u>Answer :-</u>The solution for the given problem is (1/2,1/3)

<u>Check</u>: If x = 1/2 and y = 1/3 then

LHS = (2/x)+(3/y)

= 2/(1/2)+3/(1/3)

= (2×2)+(3×3)

= 4+9

= 13

= RHS

LHS=RHS is true

and

LHS=(5/x)-(4/y)

⇛ 5/(1/2)- 4/(1/3)

⇛(5×2)-(4×3)

⇛ 10-12

⇛ -2

⇛RHS

LHS = RHS is true

5 0
2 years ago
Plz help this is due tonight
andrew-mc [135]
3(10g + 6y)

3(10g) +3 (6y)

30g + 18y

option 2
6 0
3 years ago
Read 2 more answers
Help me please! If you DO decide to help, please explain it to me since I'm extremely confused! THANK YOU!
den301095 [7]

\bf \cfrac{(-4x^2)(2x^{-2}y)^3}{(16x^5)(4y^3)^2}\implies \cfrac{(-4x^2)(2^3x^{-2\cdot 3}y^3)}{(16x^5)(4^2y^{3\cdot 2})}\implies \cfrac{(-4x^2)(8x^{-6}y^3)}{(16x^5)(16y^6)} \\\\\\ \cfrac{-32x^{2-6}y^3}{256x^5y^6}\implies -\cfrac{x^{-4} y^3}{8x^5y^6}\implies -\cfrac{1}{8x^5x^{4}y^6y^{-3}}\implies -\cfrac{1}{8x^{5+4}y^{6-3}} \\\\\\ -\cfrac{1}{8x^9y^3}

8 0
3 years ago
Read 2 more answers
I will give brainliest if you answer this question!!
AnnZ [28]

A,C,D

"B" is definitely not the answer because the fraction isn't negative but the decimal is negative which isn't right.

4 0
3 years ago
Read 2 more answers
if the focus of an ellipse are (-4,4) and (6,4), then the coordinates of the enter of the ellipsis are
STALIN [3.7K]
I’m sorry but I literally dunno
6 0
3 years ago
Read 2 more answers
Other questions:
  • An art gallery sells paintings at $0.35 per square inch.If a painting is 2 feet 3 inches by 3 feet 5 inches, how much would the
    6·1 answer
  • Whats kjfsjfhafkjsfvkasvkasfjgajsf 10 + 2
    12·2 answers
  • Which number line represents the solution of 5x + 3 ≤ -7? A) A B) B C) C D) D
    10·1 answer
  • What the answer question
    5·1 answer
  • A boat traveled -3.4 mph for 0.75 hours. How far did it go?
    12·1 answer
  • Find the area of the circle when C = π/6 . Give your answer in terms of π.
    13·1 answer
  • Simplify this fraction: <br> 2160/10
    12·2 answers
  • Han wears a hat to school every 4th day and a jacket every 6th day. What will be the first day that Han wears a hat and a jacket
    7·2 answers
  • If the point (7,1757,175) lies on the graph, what does the ordered pair (7,1757,175) indicate?
    9·2 answers
  • Please help! <br> what is the value of x, y, and z?
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!