tha area of a regular octagon found by decomposing the octagon into a rectangle into trapezoids is ________ m2
To find the area of a regular octagon by decomposing it into a rectangle and trapezoids, you need to know the length of one side of the octagon or the apothem (a line drawn from the center of the octagon to the midpoint of one of its sides). Let's assume we know the length of one side of the octagon.
Here are the steps to find the area:
1. Calculate the area of the rectangle: The rectangle is formed by extending the two adjacent sides of the octagon. The length of the rectangle is equal to the side length, and the width is determined by the apothem. The formula to find the area of a rectangle is Area = length × width.
2. Calculate the area of each trapezoid: The trapezoids are formed by the remaining slanted sides of the octagon. The formula to find the area of a trapezoid is Area = ((base1 + base2) / 2) × height. In this case, both bases will have the length of the side of the octagon, and the height will be the length of the apothem.
3. Add the area of the rectangle to the sum of the areas of the trapezoids to get the total area of the octagon.
Let's say the length of one side of the octagon is "s" and the length of the apothem is "a". The area can be expressed as:
Area = (length of rectangle) × (width of rectangle) + (area of trapezoid 1) + (area of trapezoid 2) + ... + (area of trapezoid 8)
Area = s × 2a + ((s + s) / 2) × a + ((s + s) / 2) × a + ... + ((s + s) / 2) × a
Area = 2s × a + 4s × a
Area = 6s × a
Therefore, the area of a regular octagon found by decomposing it into a rectangle and trapezoids is 6s × a square units.