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The answer depends on the nature of the complex shape. Some complex shapes can be decomposed into smaller shapes whose areas can be determined using standard formulae. It is then simply a question of adding the parts together.

For more complicated shapes, there are essentially two options: you can either use uniform laminae and mass or estimate the area using grids.

Uniform Lamina: Copy the shape onto a sheet (lamina) of material with uniform density. Cut the shape out carefully and measure its mass (or weight). Do the same for a unit square of the lamina.

Then, because the lamina is of uniform density, the ratio of the two areas is the same as the ratio of the two masses.

That is: Area of Shape/Area of Unit Square = Mass of Shape/Mass of Unit Square.

Rearranging, and noting that the area of the Unit Square is, by definition, = 1 sq unit

Area of Shape = Mass of Shape/Mass of Unit Square.

Grid Method: Copy the shape onto a grid, where each grid square has an area of G square units. Count the number of squares that are fully or mostly inside the shape. Call this number W (for whole). Count the number of squares that are approximately half inside the shape and call this number H (for half). Ignore any square that are less than half in the shape.

Then a reasonable estimate of the area of the shape is G*[W + H/2] square units. There is some arbitrariness about "mostly inside" and "approximately half" but there is no way around that. You will get more accurate results with finer grids, but they will also require much more effort in terms of counting the grid squares.

Q: How do you find area compound shape?

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You partition the compound shape into simpler shapes whose areas you can work out using formulae, and then add all those parts together.

You would find the area of the inside and outside shape (pretending that the inside shape was not in the outside shape). then, you would take the area of the outside shape and subtract the area of the inside shape.

Shape of what ?

To find the area, first divide the shape into regular, simple shapes. Then use formulas to find the area of the smaller, regular shapes. Lastly, add up all the smaller areas to find the area of the original shape.

Such as? If you can break the shape up into triangles you can find the area that way. Or, you can get into calculus-based equations if you have an equation for the random shape.

Related questions

You partition the compound shape into simpler shapes whose areas you can work out using formulae, and then add all those parts together.

You would find the area of the inside and outside shape (pretending that the inside shape was not in the outside shape). then, you would take the area of the outside shape and subtract the area of the inside shape.

Shape of what ?

To find the area, first divide the shape into regular, simple shapes. Then use formulas to find the area of the smaller, regular shapes. Lastly, add up all the smaller areas to find the area of the original shape.

Such as? If you can break the shape up into triangles you can find the area that way. Or, you can get into calculus-based equations if you have an equation for the random shape.

Fill in the blanks so that the shape makes a square and find the area of that. Then find the area of the shape you added. When you have both areas, subtract the greater from the smaller.

You times the length by width, to get the area of the 2D shape.

To find the area, first divide the shape into regular, simple shapes. Then use formulas to find the area of the smaller, regular shapes. Lastly, add up all the smaller areas to find the area of the original shape.

To find the area, first divide the shape into regular, simple shapes. Then use formulas to find the area of the smaller, regular shapes. Then add up all the areas to find the area of the original shape.