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Gennadij [26K]
3 years ago
8

What is the surface area of the right prism given below?

Mathematics
2 answers:
mihalych1998 [28]3 years ago
7 0

For this case, we have that the area of the surface of the figure shown is given by:

A_{1}: The area of the upper rectangle (inclined)

A_{2}: The area of the two triangles.

A_{3}: The area of the base of the prism

A_ {4}: The area of the rear rectangle

We apply Pythagoras to know the length of the inclined side of the rectangle:

h = \sqrt {15 ^ 2 + 8 ^ 2}\\h = \sqrt {289}\\h = 17 \ units

Thus, the A_{1} is given by:

A_ {1} = 10 * 17\\A_ {1} = 170 \ units ^ 2

We look for the area given by the triangles, knowing that the area of a triangle is \frac {1} {2} b * h, then:

A_ {2} = \frac {1} {2} b * h + \frac {1} {2} b * h\\A_ {2} = b * h\\A _{2} = 15 * 8\\A_{2} = 120 \ units ^ 2

We look for the area of the base of the prism:

A_ {3} = 10 * 15\\A_ {3} = 150 \ units ^ 2

We look for the area of the posterior rectangle:

A_ {4} = 8 * 10\\\A_ {4} = 80 \ units ^ 2

Adding we have:

A_ {t} = (170 + 120 + 150 + 80) \ units ^ 2\\A_ {t} = 520 \ units ^ 2

Answer:

520 \ units ^ 2

Sloan [31]3 years ago
3 0

Answer:

10*15= 150

150 *8= 1,200

1,200 ÷ 2 = 600.

Step-by-step explanation:


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C. 17.6

General Formulas and Concepts:

<u>Math</u>

  • Rounding

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Trigonometry</u>

  • [Right Triangles Only] SOHCAHTOA
  • [Right Triangles Only] tanθ = opposite over adjacent

Step-by-step explanation:

<u>Step 1: Identify Variables</u>

Angle θ = 40°

Opposite Leg = <em>x</em>

Adjacent Leg = 21

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Substitute in variables [tangent]:                                                                   \displaystyle tan(40^\circ) = \frac{x}{21}
  2. [Multiplication Property of Equality] Isolate <em>x</em>:                                                \displaystyle 21tan(40^\circ) = x
  3. Rewrite:                                                                                                           \displaystyle x = 21tan(40^\circ)
  4. Evaluate:                                                                                                          \displaystyle x = 17.6211
  5. Round:                                                                                                            \displaystyle x \approx 17.6
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