Assuming the vertex of the triangle shown is the center of the pentagon, and the line segment shown is an altitude of the triangle:
If we join the center of (the circumscribed circle and of) the pentagon to the 5 vertices, 5 isosceles triangles are formed, all congruent to the one shown in the figure. It is clear that these triangles are congruent, so to find the area of the pentagon, we find the area of one of these triangles and multiply by 5.
The base of the triangle is 22.3 in, and the height is 15.4 ins, thus the area of the pentagon is:
5(Area triangle)=5*[(22.3*15.4)/2]=<span>858.55 (square inches).
Answer: </span>858.55 (square inches).
Distance = rate x time
Distance = 221 miles
Rate = 68 mph
221 miles = 68 mph x time
221 miles/68 mph = time
3.25 hours = time
Answer:
5.4332, 7.7, 7.03, and then 7.73
Answer:
a) Interest earned = $36
New Balance = $336
b) Interest rate = 0.05 or 5%
New Balance = $517.5
c) time t = 5
New Balance = $612.5
d) Principal Amount = $675
New Balance = $783
Step-by-step explanation:
We are given:
a) Principal (P) = $300
Rate (r) = 3% or 0.03
Time (t)= 4 years
Interest earned = ?
The formula used is: ![Simple \ Interest (I)= P\times r\times t](https://tex.z-dn.net/?f=Simple%20%5C%20Interest%20%28I%29%3D%20P%5Ctimes%20r%5Ctimes%20t)
Putting values and finding interest
![Simple \ Interest (I)= P\times r\times t\\Simple \ Interest (I)= 300\times 0.03\times 4\\Simple \ Interest (I)= 36](https://tex.z-dn.net/?f=Simple%20%5C%20Interest%20%28I%29%3D%20P%5Ctimes%20r%5Ctimes%20t%5C%5CSimple%20%5C%20Interest%20%28I%29%3D%20300%5Ctimes%200.03%5Ctimes%204%5C%5CSimple%20%5C%20Interest%20%28I%29%3D%2036)
So, Interest earned = $36
New Balance = Principal + Interest = 300+36 = $336
b) a) Principal (P) = $300
Rate (r) = ?
Time (t)= 3 years
Interest earned = 67.50
The formula used is: ![Simple \ Interest (I)= P\times r\times t](https://tex.z-dn.net/?f=Simple%20%5C%20Interest%20%28I%29%3D%20P%5Ctimes%20r%5Ctimes%20t)
Putting values and finding rate
![Simple \ Interest (I)= P\times r\times t\\67.50= 450\times r\times 3\\67.50=1350\times r\\r=\frac{67.50}{1350}\\r=0.05 \ or \ 5\%](https://tex.z-dn.net/?f=Simple%20%5C%20Interest%20%28I%29%3D%20P%5Ctimes%20r%5Ctimes%20t%5C%5C67.50%3D%20450%5Ctimes%20r%5Ctimes%203%5C%5C67.50%3D1350%5Ctimes%20r%5C%5Cr%3D%5Cfrac%7B67.50%7D%7B1350%7D%5C%5Cr%3D0.05%20%5C%20or%20%5C%205%5C%25)
So, Interest rate = 0.05 or 5%
New Balance = Principal + Interest = 450+67.50 = $517.5
c) Principal (P) = $500
Rate (r) = 4.5% or 0.045
Time (t)= ?
Interest earned = $112.50
The formula used is: ![Simple \ Interest (I)= P\times r\times t](https://tex.z-dn.net/?f=Simple%20%5C%20Interest%20%28I%29%3D%20P%5Ctimes%20r%5Ctimes%20t)
Putting values and finding time
![Simple \ Interest (I)= P\times r\times t\\112.50= 500\times 0.045\times t\\112.50=22.5 \times t\\t=\frac{112.50}{22.5}\\t=5](https://tex.z-dn.net/?f=Simple%20%5C%20Interest%20%28I%29%3D%20P%5Ctimes%20r%5Ctimes%20t%5C%5C112.50%3D%20500%5Ctimes%200.045%5Ctimes%20t%5C%5C112.50%3D22.5%20%5Ctimes%20t%5C%5Ct%3D%5Cfrac%7B112.50%7D%7B22.5%7D%5C%5Ct%3D5)
So, time t = 5
New Balance = Principal + Interest = 500+112.50 = $612.5
d) Principal (P) = ?
Rate (r) = 8% or 0.08
Time (t)= 2 years
Interest earned = 108.00
The formula used is: ![Simple \ Interest (I)= P\times r\times t](https://tex.z-dn.net/?f=Simple%20%5C%20Interest%20%28I%29%3D%20P%5Ctimes%20r%5Ctimes%20t)
Putting values and finding Principal
![Simple \ Interest (I)= P\times r\times t\\108=P\times 0.08 \times 2\\108=P\times 0.16\\P=\frac{108}{0.16}\\P=675](https://tex.z-dn.net/?f=Simple%20%5C%20Interest%20%28I%29%3D%20P%5Ctimes%20r%5Ctimes%20t%5C%5C108%3DP%5Ctimes%200.08%20%5Ctimes%202%5C%5C108%3DP%5Ctimes%200.16%5C%5CP%3D%5Cfrac%7B108%7D%7B0.16%7D%5C%5CP%3D675)
So, Principal Amount = $675
New Balance = Principal + Interest = 675+108 = $783