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Black_prince [1.1K]
3 years ago
8

Find the source area of the space figure represented by the net

Mathematics
1 answer:
sergejj [24]3 years ago
6 0

I assume you meant "surface area" :)

Looking at the net, it looks like if you folded it back together it would form to become a triangular prism.

To calculate the surface area of a triangular prism, you would use the formula: A = bh + 2ls + lb, where b is the base of the triangular faces, h is the height of the prism, l is the length of the prism, and s is the side length of the prism.

I attached a picture to help you see what these labels are.

Looking at the diagram you've provided, we can assume that b = 7 cm, h = 4 cm, l = 8 cm, and s = 5 cm. Substitute these into the formula.

A = bh + 2ls + lb ==> A = (7)(4) + 2(8)(5) + (8)(7)

Multiply from left to right.

28 + 80 + 56

Add.

164

The surface area of this triangular prism is A) 164 cm^2.

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atroni [7]

Answer:

  (x, y, z) = (3, -2, 4)

Step-by-step explanation:

The attachment shows a solution using a graphing calculator where the first equation is solved for z, and that expression is substituted into each of the other two equations. The solution to that system is (x, y) = (3, -2). Using these values in the expression for z, we find ...

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Your graphing calculator and/or online tools can give you the reduced row echelon form of the augmented matrix representing the system:

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If you're solving by hand, you can do the substitution described above to eliminate z from one equation. You can eliminate z from another equation by adding the last two:

  -3x -4y +4(5 -x -y) = 15   ⇒   -7x -8y = -5

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  -7(-5y -7) -8y = -5   ⇒   27y = -54   ⇒   y = -2

  x = -5(-2) -7 = 3

  z = 5 -(3) -(-2) = 4

_____

<em>Additional comment</em>

If all that is needed is a solution, we prefer a graphical or matrix approach. These take about the same amount of time. Both require a little additional effort to determine exact values when the solutions are not integers.

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