Answer:
Option B)
Step-by-step explanation:
We already know that:
- Given height of trapezoid: 4 units
- Given base(s) of trapezoid: (x + 7) and (x - 3) units
Formula to determine the area of a trapezoid:
[tex]\boxed{\large\text{Area of trapezoid formula:}\ \dfrac{(\text{Base}_{1} + \text{Base}_{2})\text{(h)}}{2}}[/tex]
Substitute the base(s) and the height in the formula;
[tex]\bullet \implies\text{Area of trapezoid} = \dfrac{[(x - 3) + (x + 7)]\text{(4)}}{2}}[/tex]
Simplifiy the distributive property in the numerator;
[tex]\bullet \implies\text{Area of trapezoid} = \dfrac{[4(x - 3) + 4(x + 7)]}{2}}[/tex]
[tex]\bullet \implies\text{Area of trapezoid} = \dfrac{[4x - 12 + 4x + 28]}{2}}[/tex]
[tex]\bullet \implies\text{Area of trapezoid} = \dfrac{8x + 16}{2}}[/tex]
Distribute the denominators and simplify;
[tex]\bullet \implies\text{Area of trapezoid} = \dfrac{8x}{2}} + \dfrac{16}{2}[/tex]
[tex]\bullet \implies\boxed{\text{Area of trapezoid} = 4x + 8 \ \text{units}^{2}}[/tex]
The area of trapezoid stated above, matches with option B.
Therefore, Option B is correct.
