Answer:
[tex]\large \boxed{\text{D. 126.2 cm}^{2}}[/tex]
Step-by-step explanation:
The area left over for scrap is the area of the circle minus the area of the hexagon.
1. Area of circle
The formula for the area of a circle is
A = πr²
A = π(6)² = 36π = 113.1 in²
2. Area of hexagon
A hexagon consists of six equilateral triangles, each of side a, and we can divide each of them into two right triangles.
So, we can calculate the area of one right triangle and multiply by 12.
The formula for the area of one triangle is
A = ½bh
(a) Height of a small triangle
Per the Pythagorean Theorem,
[tex]\begin{array}{rcr}h^{2} + 3^{2} & = & 6^{2}\\h^{2} + 9 & = & 36\\h^{2} & = & 27\\& = & 3\sqrt{3}\\\end{array}\\[/tex]
(b) Area of a small triangle
A = ½ bh = ½ × 3 × 3√3 = 4.5√3 in²
(c) Area of the hexagon
The hexagon contains 12 small triangles.
A = 12 × 4.5√ 3 = 54√3 ≈ 93.53 in²
3. Area of scrap
A ≈ 113.1 in² - 93.53 in² = 19.6 in²
[tex]A = \text{19.6 in}^{2} \times \left(\dfrac{\text{2.54 cm}}{\text{1 in}}\right )^{2} = \text{126.2 cm}^{2}\\\\\text{The area of the scrap is $\large \boxed{\textbf{126.2 cm}^{\mathbf{2}}}$}[/tex]
