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Area of an equilateral triangle is 
, where s is length of a side; we have s = 2 + 4 + 2 = 8 mm; then area is 
;
Area of a semi-circle = (1/2)π
, where r is the radius of circle; r = 4/2 = 2 mm; then area is 2π;
The shaded area is![16 \sqrt{3} - 2π = 2( [tex]8 \sqrt{3}](https://tex.z-dn.net/?f=16%20%5Csqrt%7B3%7D%20-%202%CF%80%20%3D%202%28%20%5Btex%5D8%20%5Csqrt%7B3%7D%20)
- π );
Area of a semi-circle = (1/2)π
The shaded area is
The <em>first three</em> elements of the <em>recursive</em> series are 6, 10, 8. (Correct choice: B)
<h3>How to generate values from a recursive function</h3>
In this question we have a kind of <em>recursive</em> function known as Fibonacci's function, where a value of the series is generated from at least <em>immediately previous</em> elements. In this case, we need to find the <em>first</em> three elements from the <em>fifth</em> and <em>fourth</em> elements of the series:
a₄ = a₅ - a₆ + 4
a₄ = - 2 - 0 + 4
a₄ = 2
a₃ = a₄ - a₅ + 4
a₃ = 2 - (- 2) + 4
a₃ = 8
a₂ = a₃ - a₄ + 4
a₂ = 8 - 2 + 4
a₂ = 10
a₁ = a₂ - a₃ + 4
a₁ = 10 - 8 + 4
a₁ = 6
The <em>first three</em> elements of the <em>recursive</em> series are 6, 10, 8. (Correct choice: B)
To learn more on recursive series: brainly.com/question/8972906
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