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Nastasia [14]
3 years ago
9

The logo for Chris's Calculator Company is 3 semicircles. The logo will be placed on the company building and will be 4 feet tal

l. What is the area of the logo?
18.84 ft2
37.68 ft2
50.24 ft2
75.36 ft2

Mathematics
1 answer:
Keith_Richards [23]3 years ago
8 0

Answer:

The area of the logo is 18.84\ ft^{2}

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The area of a semicircle is equal to

A=\frac{1}{2}\pi r^{2}

so

The area of the logo is equal to multiply by 3 the area of one semicircle

A=\frac{3}{2}\pi r^{2}

we have

r=4/2=2\ ft -----> the radius is half the diameter

substitute

A=\frac{3}{2}(3.14)(2)^{2}=18.84\ ft^{2}

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The number that belongs <em>in</em> the green box is equal to 909.

General Formulas and Concepts:
<u>Algebra I</u>

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

<u>Trigonometry</u>

[<em>Right Triangles Only</em>] Pythagorean Theorem:
\displaystyle a^2 + b^2 = c^2

  • a is a leg
  • b is another leg
  • c is the hypotenuse

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify given variables</em>.

<em>a</em> = 30

<em>b</em> = 3

<em>c</em> = <em>x</em>

<em />

<u>Step 2: Find </u><u><em>x</em></u>

Let's solve for the <em>general</em> equation that allows us to find the hypotenuse:

  1. [Pythagorean Theorem] Square root both sides [Equality Property]:
    \displaystyle \begin{aligned}a^2 + b^2 = c^2 \rightarrow c = \sqrt{a^2 + b^2}\end{aligned}

Now that we have the <em>formula</em> to solve for the hypotenuse, let's figure out what <em>x</em> is equal to:

  1. [Equation] <em>Substitute</em> in variables:
    \displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2}\end{aligned}
  2. <em>Evaluate</em>:
    \displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2} \\& = \boxed{ \sqrt{909} } \\\end{aligned}

∴ the hypotenuse length <em>x</em> is equal to √909 and the number <em>under</em> the square root, our answer, is equal to 909.

___

Learn more about Trigonometry: brainly.com/question/27707750

___

Topic: Trigonometry

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