Question

area of a pentagon with numbers 4, 6, 16, 9

Answer 1

whats the answer

Answer 2

To find the area of a pentagon with these side lengths, we first need to calculate the apothem (the distance from the center of the pentagon to the midpoint of one of its sides).

To do this, we can use the formula for the apothem of a regular pentagon:

apothem = side length / (2 * tan(π/5))

Given that the side lengths are 4, 6, 16, 9, we can calculate the apothem for each side length and take their average as the apothem for the pentagon:

For side length 4:
apothem_4 = 4 / (2 * tan(π/5))

For side length 6:
apothem_6 = 6 / (2 * tan(π/5))

For side length 16:
apothem_16 = 16 / (2 * tan(π/5))

For side length 9:
apothem_9 = 9 / (2 * tan(π/5))

Now, find the average of the four apothems:

Average apothem = (apothem_4 + apothem_6 + apothem_16 + apothem_9) / 4

Once you have the apothem, you can use the formula for the area of a regular pentagon:

area = 5/2 * apothem * side length

Calculate the area using the apothem and one of the side lengths.

Answer 3

To find the apothem for the given side lengths of 4, 6, 16, and 9, we need to calculate it individually for each side length as follows:

For side length 4:
apothem_4 = 4 / (2 * tan(π/5)) ≈ 1.47

For side length 6:
apothem_6 = 6 / (2 * tan(π/5)) ≈ 2.21

For side length 16:
apothem_16 = 16 / (2 * tan(π/5)) ≈ 5.88

For side length 9:
apothem_9 = 9 / (2 * tan(π/5)) ≈ 3.33

Now, find the average of the four apothems:

Average apothem = (1.47 + 2.21 + 5.88 + 3.33) / 4 ≈ 3.22

Using the formula for the area of a regular pentagon:

area = 5/2 * apothem * side length

Let's take the side length of 9 to calculate the area:

area = 5/2 * 3.22 * 9 ≈ 72.45

So, the area of the pentagon with side lengths 4, 6, 16, and 9 is approximately 72.45 square units.