What is the area of a shape that that has 8 sides and has 1 , 1 , 8 , 1 , 1 , 3 , 3 and 10 as the lengths of the 8 sides?
To find the area of a shape with 8 sides and given lengths, we need to first determine the type of shape. In this case, we can identify the shape as an irregular octagon since it has eight sides of different lengths.
To find the area of an irregular octagon, we can divide it into smaller shapes (triangles and rectangles) whose areas can be calculated individually. There are different methods to calculate the area of an irregular octagon, but in this explanation, we will use the method of dividing it into triangles and rectangles.
Here are the steps to find the area of an irregular octagon:
1. Draw the irregular octagon:
- Start by drawing a rough sketch of the given octagon, labeling the side lengths: 1, 1, 8, 1, 1, 3, 3, and 10.
2. Divide the irregular octagon:
- Identify the diagonals of the octagon that can divide it into triangles and rectangles.
- In this case, we can draw two diagonals from opposite corners, dividing the octagon into four triangles and four rectangles.
3. Calculate the area of each shape:
- Since all the side lengths are given, we can calculate the area of each triangle and rectangle using their respective formulas:
- Triangle area formula: A = (base * height) / 2
- Rectangle area formula: A = length * width
- Substitute the given side lengths into the formulas for each triangle and rectangle.
4. Sum up the areas:
- Add up the areas of all the triangles and rectangles to get the total area of the irregular octagon.
Following these steps, calculate the area of each shape and sum them up to find the area of the irregular octagon with side lengths 1, 1, 8, 1, 1, 3, 3, and 10.