To find the perimeter and areas of complex shape without a grid you should divide the shape into simple shapes and find the area of each shape alone and then add up the areas all together to get the area of the whole shape. Example: If there is a shape that can be divided into 2 triangles and 1 rectangle then you will find the area of each triangle alone and then the area of the rectangle then add up all the areas together.
You don't need to if you can manage to work out the perimeter and area of complex shapes. Most people cannot work easily with shapes other than triangles, quadrilaterals, circles and semicircles. For them (us) it is easier to partition the shape.
Most shapes have different perimeter than area, as far as value.
Yes - even shapes with different area.
There is no perimeter of a circle. Only flat shapes have perimeters. You can however, find the circumference, surface area, and volume.
You can't. The perimeter doesn't tell the area. There are an infinite number of shapes with different dimensions and different areas that all have the same perimeter.
An area can increase while the perimeter decreases in certain geometric shapes, particularly when transitioning from more complex shapes to simpler ones. For example, if you take a shape like an irregular polygon and gradually round its corners or smooth its edges, the overall area can increase while the perimeter shrinks. This phenomenon highlights the relationship between area and perimeter in geometric transformations.
Anywhere between 0 square feet and approx 998.2 square feet - it all depends upon the exact shape of the complex figure. To calculate the area of a complex figure, split it up into shapes for which you can workout the area and then add all the areas of the shapes together.
You don't need to if you can manage to work out the perimeter and area of complex shapes. Most people cannot work easily with shapes other than triangles, quadrilaterals, circles and semicircles. For them (us) it is easier to partition the shape.
Most shapes have different perimeter than area, as far as value.
Yes - even shapes with different area.
There are infinitely many shapes.
yes they can
There is no perimeter of a circle. Only flat shapes have perimeters. You can however, find the circumference, surface area, and volume.
You can't. The perimeter doesn't tell the area. There are an infinite number of shapes with different dimensions and different areas that all have the same perimeter.
To find the perimeter when you know the area, you typically need additional information about the shape in question, as multiple shapes can have the same area but different perimeters. For example, if you have a rectangle, knowing the area allows you to express one dimension in terms of the other, and you can then calculate the perimeter using the formula ( P = 2(l + w) ). For regular shapes like squares, you can directly derive the perimeter from the area; for example, if the area of a square is ( A ), the side length ( s ) is ( s = \sqrt{A} ), and the perimeter is ( P = 4s ). However, without knowing the specific shape or additional parameters, you cannot determine the perimeter solely from the area.
Because the area is different than the perimeters
They are physical characteristics of a plane shape. 3-dimensional shapes do have areas, but the concept of a perimeter is generally restricted to plane shapes.