Answer:
you can't cheat in an online school math test =_=
Step-by-step explanation:
<h3>Given</h3>
1) Trapezoid BEAR with bases 11.5 and 6.5 and height 8.5, all in cm.
2) Regular pentagon PENTA with side lengths 9 m
<h3>Find</h3>
The area of each figure, rounded to the nearest integer
<h3>Solution</h3>
1) The area of a trapezoid is given by
... A = (1/2)(b1 +b2)h
... A = (1/2)(11.5 +6.5)·(8.5) = 76.5 ≈ 77
The area of BEAR is about 77 cm².
2) The conventional formula for the area of a regular polygon makes use of its perimeter and the length of the apothem. For an n-sided polygon with side length s, the perimeter is p = n·s. The length of the apothem is found using trigonometry to be a = (s/2)/tan(180°/n). Then the area is ...
... A = (1/2)ap
... A = (1/2)(s/(2tan(180°/n)))(ns)
... A = (n/4)s²/tan(180°/n)
We have a polygon with s=9 and n=5, so its area is
... A = (5/4)·9²/tan(36°) ≈ 139.36
The area of PENTA is about 139 m².
Answer:
Center: (0, 0)
Radius: 4
Step-by-step explanation:
Circle Standard Equation: (x - h)² + (y - k)² = r²
(h, k) is center
r is radius
We see that our <em>h</em> and our <em>k</em> are both 0.
∴ Our center is (0, 0), origin.
We see that our r² = 16
√r² = √16
∴ Our radius is equal to 4
The wall area is the product of the room perimeter and the room height:
A₁ = (2*(12.5 ft + 10.5 ft))*(8.0 ft) = 368 ft²
The window and door area together is
A₂ = 2*((4 ft)*(3 ft)) + (7 ft)*(3 ft) = 45 ft²
The area of one roll of wallpaper is
A₃ = (2.5 ft)*(30 ft) = 75 ft²
Then the number of rolls of wallpaper required will be
1.1*(A₁ - A₂)/A₃ ≈ 4.74
5 rolls of wallpaper should be purchased.
_____
As a practical matter, not much of the window and door area can be saved. The rolls are 30 inches wide, but the openings are 36 inches wide. Some will likely have to be cut from two strips. The strips will have to be the full length of the wall, and the amount cut likely cannot be used elsewhere. If the window and door area cannot be salvaged, then likely ceiling(5.4) = 6 rolls will be needed (still allowing 10% for matching and waste).
Answer: sounds interesting
Step-by-step explanation:
