AFB = CFD = 31
BFC = 90 - (31+31) = 28
DFE = BFC = 28
CFE = CFD + DFE = 31 + 28 = 59
Answer:
![\large \boxed{\text{101 pieces}}](https://tex.z-dn.net/?f=%5Clarge%20%5Cboxed%7B%5Ctext%7B101%20pieces%7D%7D)
Step-by-step explanation:
1. Calculate the area of the floor
The formula for the area of a trapezoid is
A = ½(a + b)h,
where a and b are the lengths of the parallel sides and h is the distance between them.
However, we are not given the value of h, so we must use Brahmagupta's formula.
If the four sides are a, b, c, and d, the area A is
![A = \sqrt{(s - a) (s - b) (s - c) (s - d)}](https://tex.z-dn.net/?f=A%20%3D%20%5Csqrt%7B%28s%20-%20a%29%20%28s%20-%20b%29%20%28s%20-%20c%29%20%28s%20-%20d%29%7D)
where s is the semiperimeter
![s = \frac{1}{2}(a + b + c + d)](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28a%20%2B%20b%20%2B%20c%20%2B%20d%29)
Data:
a = 13 ft
b = 16 ft
c = 13 ft
d = 26 ft
(a) Calculate the semiperimeter
![\begin{array}{rcl}s & = & \sqrt{(s - a) (s - b) (s - c) (s - d)}\\\\ & = & \frac{1}{2}(13 + 16 + 13 + 26)\\\\ & = & \frac{1}{2}(68)\\\\ & = & 34\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7Ds%20%26%20%3D%20%26%20%5Csqrt%7B%28s%20-%20a%29%20%28s%20-%20b%29%20%28s%20-%20c%29%20%28s%20-%20d%29%7D%5C%5C%5C%5C%20%26%20%3D%20%26%20%5Cfrac%7B1%7D%7B2%7D%2813%20%2B%2016%20%2B%2013%20%2B%2026%29%5C%5C%5C%5C%20%26%20%3D%20%26%20%5Cfrac%7B1%7D%7B2%7D%2868%29%5C%5C%5C%5C%20%26%20%3D%20%26%2034%5C%5C%5Cend%7Barray%7D)
(b) Calculate the area
![\begin{array}{rcl}A & = &\sqrt{(s - a) (s - b) (s - c) (s - d)}\\\\& = &\sqrt{(34 - 13) (34 - 16) (34 - 13) (34 - 26)}\\\\& = &\sqrt{21 \times 18 \times 21 \times 8}\\\\& = & \sqrt{63504}\\\\ & = & \mathbf{252}\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7DA%20%26%20%3D%20%26%5Csqrt%7B%28s%20-%20a%29%20%28s%20-%20b%29%20%28s%20-%20c%29%20%28s%20-%20d%29%7D%5C%5C%5C%5C%26%20%3D%20%26%5Csqrt%7B%2834%20-%2013%29%20%2834%20-%2016%29%20%2834%20-%2013%29%20%2834%20-%2026%29%7D%5C%5C%5C%5C%26%20%3D%20%26%5Csqrt%7B21%20%5Ctimes%2018%20%5Ctimes%2021%20%5Ctimes%208%7D%5C%5C%5C%5C%26%20%3D%20%26%20%5Csqrt%7B63504%7D%5C%5C%5C%5C%20%26%20%3D%20%26%20%5Cmathbf%7B252%7D%5C%5C%5Cend%7Barray%7D)
The area of David's floor is 252 ft².
2. Calculate the number of pieces of material
![\text{No. of pieces} = \text{252 ft}^{2} \times \dfrac{\text{1 piece}}{\text{2.5 ft}^{2}} = \textbf{100.8 pieces}\\\\\text{David can't buy a fraction of a piece, so he must buy $\large \boxed{\textbf{101 pieces}}$}](https://tex.z-dn.net/?f=%5Ctext%7BNo.%20of%20pieces%7D%20%3D%20%5Ctext%7B252%20ft%7D%5E%7B2%7D%20%5Ctimes%20%5Cdfrac%7B%5Ctext%7B1%20piece%7D%7D%7B%5Ctext%7B2.5%20ft%7D%5E%7B2%7D%7D%20%3D%20%5Ctextbf%7B100.8%20pieces%7D%5C%5C%5C%5C%5Ctext%7BDavid%20can%27t%20buy%20a%20fraction%20of%20a%20piece%2C%20so%20he%20must%20buy%20%24%5Clarge%20%5Cboxed%7B%5Ctextbf%7B101%20pieces%7D%7D%24%7D)
Answer:
5. (a)
6. (b)
I am hoping that this will help you
Hello! To answer this question, all you have to do is divide the amount traveled by the speed per second. 200/5 is 40. It would take 40 seconds to travel 200 meters.
The most logical answer is: <span>B. Maria knows they traveled 200 miles altogether. She knows they drove for 4 hours. She does not know how many miles they drove each hour.</span>