How do you do area for an irregular shape?

Answer 1

There are three main methods:

Method 1: The simplest situation is one in which the irregular shape can be divided up into shapes whose areas can be calculated. For example, the outline of an ice-cream cone may be viewed as a triangle with a semi-circle on top. So calculate the areas for the bits and add them up.

Method 2: Trace the shape onto dense lamina of uniform thickness. Cut out the shape and measure its mass. Next cut out a UNIT square of the same lamina and measure its mass.

Then

Area of irregular shape = Mass of irregular lamina/Mass of lamina square.

Method 3: Trace the shape onto a sheet of paper with square gridlines on it. Count the number of whole (or almost whole) squares inside the shape = A. Count the number of squares where approximately half is inside the area = B. Ignore all squares where only a tiny bit is in the marked area.

Then,

Area of irregular shape = (A+B/2)*area of unit square in the grid.

The finer the grid, the more accurate your result, but also the harder you'll have to work.