a regular pentagon has an apothem of 3.2 and an area of 37.2 cm. What is the length of one side of the pentagon?
1: 45°
2: 67.5°
3 (this one): 4.65 m
4: 288 cm²
5: 150sqrt3 in.²
the answer is 4.65 because I took the quick check and it was right.
@E is 100% correct :)
@E is correct
To find the length of one side of a regular pentagon, we can use the following formula:
Side Length = (2 * apothem) / tan(360° / number of sides)
In this case, the apothem is given as 3.2 cm and the number of sides of a regular pentagon is 5. Let's substitute these values into the formula and solve for the side length.
Side Length = (2 * 3.2) / tan(360° / 5)
To calculate the tangent of an angle in degrees, we need to convert the angle to radians. 360° is equal to 2π radians. So, 360° / 5 = 72°, which is equal to (72 * π) / 180 radians.
Side Length = (2 * 3.2) / tan((72 * π) / 180)
Now, let's use a calculator to find the approximate value of the tangent and solve the equation:
tan((72 * π) / 180) ≈ 1.376381920471173
Side Length = (2 * 3.2) / 1.376381920471173
Side Length ≈ 4.6526 cm
Therefore, the length of one side of the pentagon is approximately 4.6526 cm.
Or, using the formula area = 1/2 * apothem * perimeter,
that will give you the perimeter. 1/5 of that will be the side length.
area of one triangle = 37.2/5 = 7.44 cm
area = (1/2)base x height
7.44 = (1/2)(base)(3.2)
base = 2(7.44)/3.2)
= ...