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3 years ago

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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Solve the system of equations: X+y+z=5 -3x-4y+4z=15 2x-y-4z=-8

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 ...

z = 5 -(3 +(-2)) = 4

The solution is (x, y, z) = (3, -2, 4).

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

$\left[\begin{array}{ccc|c}1&1&1&5\\-3&-4&4&15\\2&-1&-4&-8\end{array}\right]$

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

(-3x -4y +4z) +(2x -y -4z) = (15) +(-8) ⇒ -x -5y = 7

This pair of equations can be solved for x and y in any of the usual ways. Using the second equation to substitute for x, for example, gives you ...

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

x = -5(-2) -7 = 3

z = 5 -(3) -(-2) = 4

_____

Additional comment

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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