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____ [38]
3 years ago
11

Find the area of the polygon

Mathematics
1 answer:
Helen [10]3 years ago
8 0

Answer:

Step-by-step explanation:

Assuming a perpendicular line(apotherm) is extended from the midpoint of the polygon to the midpoint of one of its sides, then we can determine the length of the apotherm by applying Pythagorean theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Let a represent the apotherm

Hypotenuse = 4

Apotherm = a

Opposite = a(apotherm = length of each side/2)

Therefore,

4² = a² + a²

16 = 2a²

a² = 16/2 = 8

a = √8 = 2√2

The formula for determining the area of a polygon is expressed as

Area = a² × n × tan 180/n

Where n represents the number of sides of the polygon.

n = 6

Therefore,

Area = (2√2)² × 6 × tan(180/6)

Area = 48 × tan 30

Area = 27.2

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Step-by-step explanation:

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3 years ago
Carlos buys a vintage automobile for $7300. He estimates that the value will increase by 3% every year. Estimate the value of th
lakkis [162]

Answer:

$9810.59

General Formulas and Concepts:

<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<u> </u>

<u>Algebra I</u>

Simple Interest Rate Formula: \displaystyle A = P(1 + r)^t

  • <em>P</em> is principle amount
  • <em>r</em> is rate
  • <em>t</em> is time (in years)

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify variables</em>

<em>P</em> = 7300

<em>r</em> = 3% = 0.03

<em>t</em> = 10

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

  1. Substitute in variables [Simple Interest Rate Formula]:                                 \displaystyle A = 7300(1 + 0.03)^{10}
  2. (Parenthesis) Add:                                                                                            \displaystyle A = 7300(1.03)^{10}
  3. Evaluate exponents:                                                                                         \displaystyle A = 7300(1.34392)
  4. Multiply:                                                                                                              \displaystyle A = 9810.59
7 0
3 years ago
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