4 5/12 Is the answer.
I hope this helps. :)
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)
1.Make a table with the x,y coordinates of each vertex. Start at any vertex and go around the polygon in either direction. Add the starting vertex again at the end. You should get a table that looks like the leftmost gray box in the figure above.
2.Combine the first two rows by:
Multiplying the first row x by the second row y. (red)
Multiplying the first row y by the second row x (blue)
Subtract the second product form the first.
3.Repeat this for rows 2 and 3, then rows 3 and 4 and so on.
4.Add these results, make it positive if required, and divide by two.
It’s really simple if you think about it
Answer:
48.8m
Step-by-step explanation:
Formula for square area =
= 148.84 ![m^{2}](https://tex.z-dn.net/?f=m%5E%7B2%7D)
=> a =
= 12.2
Formula for square perimeter = 4a = 4 x 12.2 = 48.8 m
Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
<span>y = -x3 + 5x2 - 11x + 55 ||x = 5 one root -125 + 125 - 55 + 55 = 0
using Synthetic Divsion
5 -1 5 -11 55
-5 0 -55
</span><span>-1 0 -11 0
results in:
-x^2 - 11 = 0
x^2 + 11 = 0
x^2 = -11
x = ± i√11
roots are: i√11,-i√11,5</span>