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3 years ago

What is the area of the regular polygon?

Mathematics

1 answer:

BartSMP [9]3 years ago

6 0

Answer:

You could use the polygon area formula OR here's an easier solution

We draw the lines DC and DE

Angle ADC = 120°

Triangle ADC is a 30 60 90 triangle

In such a triangle Line AE = hypotenuse * sq root (3) /2

Line AE = 3 * 0.8660254038 = 2.5980762114

Line DE = 1.5

Area of Triangle ADE = .5 * 1.5 * 2.5980762114 =

1.9485571586 square meters and entire area of Triangle

ABC = 6 * 1.9485571586

which equals 11.6913429513 square meters

Step-by-step explanation:

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Capital Value Find the capital value of an asset that generates $7200 yearly income if the interest rate is as follows.

olganol [36]

a. An asset that generates $7200 yearly income if the interest rate 5% compounded continuously, then its capital value is $140433.002

b. An asset that generates $7200 yearly income if the interest rate 10% compounded continuously, then its capital value is $68460.59

Step-by-step explanation:

For continuously compound interest

$A = P \times e^{r t}$ ---------------> eq.1

Where

P = principal amount (initial investment)

r = annual interest rate (as a decimal)

t = number of years

A = amount after time t.

Let’s solve the equation

Where,

P is unknown

A = P + 7200 (asset after 1 year) ---------------> eq. 2

Case A:

$r=\frac{\text {interest rate}}{100}=\frac{5}{100}=0.05$

t = 1 (1 year)

Substitute all values in the formula (2) using the formula (1),

$P \times e^{(0.05)(1)}=P+7200$

$P \times e^{0.05}-P=7200$

$P\left(e^{0.05}-1\right)=7200$

$P(1.05127-1)=7200$

$P(0.05127)=7200$

$P=\frac{7200}{0.05127}=\$140433.002$

Case B:

$r=\frac{\text {interest rate}}{100}=\frac{10}{100}=0.10$

t = 1 (1 year)

Substitute all values in the formula (2) using the formula (1),

$P \times e^{(0.10)(1)}=P+7200$

$P \times e^{0.10}-P=7200$

$P\left(e^{0.10}-1\right)=7200$

$P(1.10517-1)=7200$

$P(0.10517)=7200$

$P=\frac{7200}{0.10517}=\$68460.59$

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