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The answer depends on 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 could you determine the area of a shape without a formula for that shape?

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The areaof a shape is not sufficient information to determine its shape: 18000 acres could be circular, triangular, or simply an irregular shape. It could be a very long very thin rectangle, with a perimeter that is infinitely large.The only thing that can be said with certainty is that the perimeter must be at least 18.8 miles.The areaof a shape is not sufficient information to determine its shape: 18000 acres could be circular, triangular, or simply an irregular shape. It could be a very long very thin rectangle, with a perimeter that is infinitely large.The only thing that can be said with certainty is that the perimeter must be at least 18.8 miles.The areaof a shape is not sufficient information to determine its shape: 18000 acres could be circular, triangular, or simply an irregular shape. It could be a very long very thin rectangle, with a perimeter that is infinitely large.The only thing that can be said with certainty is that the perimeter must be at least 18.8 miles.The areaof a shape is not sufficient information to determine its shape: 18000 acres could be circular, triangular, or simply an irregular shape. It could be a very long very thin rectangle, with a perimeter that is infinitely large.The only thing that can be said with certainty is that the perimeter must be at least 18.8 miles.

There is no such formula. To determine the area of an irregular plane shape split it into known shapes such as rectangles, triangles, segments of a circle etc. Determine the area(s) of each of these and sum the results to find the total area.

The perimeter of a shape does not determine its area. The shape can be made thinner without changing its perimeter but reducing its area.

The perimeter of a shape does not determine its area. The shape can be made thinner without changing its perimeter but reducing its area.

The formula for the perimeter of a shape depends on the shape. It is the sum of the lengths of all the sides that enclose the shape.

Related questions

A person cannot determine the area of a shape without a formula for a composite figure. A formula must always be implemented in order to properly come with an equation.

with or without a formula

Without more information, it is impossible to determine what the amorphous object is. It could be anything without a defined shape or form, such as a pile of clothes, a blob of clay, or a spilled liquid.

The particular shape of the slot will determine how its area will be computed. The formula of area applied in calculating the area of the slot will be determined by the shape of the slot.

Substitute the information that you are given into the formula.

You cannot. The cylinder could be a large squat shape, or a thin tube which could be as long as you want. The volume of a cylinder does not determine its shape.

To calculate the volume of an arc, you first need to determine the shape of the arc (e.g., it could be a sector of a circle). Once you know the shape, use the appropriate formula for calculating the volume of that shape, such as the volume of a sector of a circle or a segment of a sphere. Calculate the volume based on the given measurements of the arc.

The areaof a shape is not sufficient information to determine its shape: 18000 acres could be circular, triangular, or simply an irregular shape. It could be a very long very thin rectangle, with a perimeter that is infinitely large.The only thing that can be said with certainty is that the perimeter must be at least 18.8 miles.The areaof a shape is not sufficient information to determine its shape: 18000 acres could be circular, triangular, or simply an irregular shape. It could be a very long very thin rectangle, with a perimeter that is infinitely large.The only thing that can be said with certainty is that the perimeter must be at least 18.8 miles.The areaof a shape is not sufficient information to determine its shape: 18000 acres could be circular, triangular, or simply an irregular shape. It could be a very long very thin rectangle, with a perimeter that is infinitely large.The only thing that can be said with certainty is that the perimeter must be at least 18.8 miles.The areaof a shape is not sufficient information to determine its shape: 18000 acres could be circular, triangular, or simply an irregular shape. It could be a very long very thin rectangle, with a perimeter that is infinitely large.The only thing that can be said with certainty is that the perimeter must be at least 18.8 miles.

There is no such formula. To determine the area of an irregular plane shape split it into known shapes such as rectangles, triangles, segments of a circle etc. Determine the area(s) of each of these and sum the results to find the total area.

The perimeter of a shape does not determine its area. The shape can be made thinner without changing its perimeter but reducing its area.

To determine the dimensions of a shape with a volume of 51.2, you would need more information about the specific shape. The volume of a shape is calculated differently based on whether it is a cube, sphere, cylinder, etc. Once you know the type of shape, you can use the appropriate formula to find the dimensions.