Answer:
A. [tex] Area = \frac{1}{2}(2x^2 - 2x - 24) [/tex]
B. [tex] Area = 3.75 in^2 [/tex]
Step-by-step explanation:
A. [tex] Area = \frac{1}{2}bh [/tex]
Where,
[tex] b = 2x + 6 [/tex]
[tex] h = x - 4 [/tex]
Plug in the values to get a polynomial that represents the area of the tool
[tex] Area = \frac{1}{2}(2x + 6)(x - 4) [/tex]
[tex] Area = \frac{1}{2}(2x(x - 4) + 6(x - 4) [/tex]
[tex] Area = \frac{1}{2}(2x^2 - 8x + 6x - 24) [/tex]
[tex] Area = \frac{1}{2}(2x^2 - 2x - 24) [/tex]
B. To find area, when x = 4.5 in, plug in the value of x into the equation for the area of the tool.
[tex] Area = \frac{1}{2}(2(4.5)2 - 2(4.5) - 24) [/tex]
[tex] Area = \frac{1}{2}(2(20.25) - 9 - 24) [/tex]
[tex] Area = \frac{1}{2}(40.5 - 9 - 24) [/tex]
[tex] Area = \frac{1}{2}(7.5) [/tex]
[tex] Area = 3.75 in^2 [/tex]
