a) To find the exact length of each side of a regular octagon, we can use the formula for the perimeter of a regular polygon:
Perimeter = number of sides x length of each side
For the regular octagon, we know that the perimeter is 450.4 cm and the number of sides is 8. Therefore:
450.4 = 8 x length of each side
Length of each side = 450.4 / 8
Length of each side = 56.3 cm
Therefore, the exact length of each side of the regular octagon is 56.3 cm.
b) To find the measure of each interior angle of a regular octagon, we can use the formula:
Interior angle = (180 * (n-2)) / n
Where n is the number of sides (which is 8 for an octagon). Plugging in n=8 into the formula, we get:
Interior angle = (180 * (8-2)) / 8
Interior angle = (180 * 6) / 8
Interior angle = 135
Therefore, the measure of each interior angle of a regular octagon is 135 degrees.
In a regular octagon, all the sides and angles are equal, so each interior angle will measure 135 degrees.
A regular octagon has a perimeter of 450.4 cm.
a) What is the exact length of each side?
b) What is the measure of each interior angle?
Explain in detail
1 answer