What is the area of a regular pentagon with a side length of 10 inches and a distance from the center to a vertex of 10 inches?

Round your answer to the nearest tenth.

Why did the regular pentagon go to the doctor?

Because it had an "acute" case of being "irregular" and needed a diagnosis!

To find the area of a regular pentagon, you can use the formula:

Area = (1/4) * sqrt(5(5 + 2 * sqrt(5))) * s^2

where s is the side length. In this case, s = 10 inches. Plugging in the values:

Area = (1/4) * sqrt(5(5 + 2 * sqrt(5))) * 10^2

After doing the calculations, I'm happy to inform you that the area of the regular pentagon is approximately 172.0 square inches. Now watch out for any irregular shapes trying to catch you off guard!

To find the area of a regular pentagon, you can use the formula:

Area = (1/4) * sqrt(5 * (5 + 2 * sqrt(5))) * side length^2

Given that the side length is 10 inches, we can substitute this value into the formula:

Area = (1/4) * sqrt(5 * (5 + 2 * sqrt(5))) * (10)^2

Now, let's calculate the value within the square root:

5 + 2 * sqrt(5) ≈ 5 + 2 * 2.236 ≈ 5 + 4.472 ≈ 9.472

Next, let's substitute this value back into the formula:

Area = (1/4) * sqrt(5 * 9.472) * (10)^2

Area = (1/4) * sqrt(47.36) * 100

To find the square root of 47.36, we get approximately 6.881.

Area = (1/4) * 6.881 * 100

Area = 1.72 * 100

Area = 172 square inches

Therefore, the area of the regular pentagon is 172 square inches.

To find the area of a regular pentagon, we can use the formula:

Area = (5/4) * S^2 * cot(π/5)

where S is the length of one side of the pentagon.

In this case, the side length is given as 10 inches.

First, let's calculate the value of cot(π/5).

cot(π/5) ≈ 0.7265

Now, we can substitute the values in the formula:

Area ≈ (5/4) * 10^2 * (0.7265)
≈ (5/4) * 100 * (0.7265)
≈ (5 * 100 * 0.7265) / 4
≈ 363.25 / 4
≈ 90.8125

Therefore, the approximate area of the regular pentagon is 90.8 square inches when rounded to the nearest tenth.

Look at one of the five isosceles triangle

each has a 72 degree angle with sides of 10 containing that angle.

Use the cosine law to find the base of that triangle
x^2 = 10^2 + 10^2 - 2(10)(10)cos 72
x = ...

Once you have that, find the area of the triangle (1/2)(10)(10sin(above angle)
then multiply by 5