What do you have to do to get a area of a shape?

Answer 1

For the area of a square and rectangle, you have to multiply the length and width (a x b). For a triangle it is 1/2 x base x height. The area of a circle is the radius squared x pie (3.14......).

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The formula for a trapezium is 1/2 *sum of parallel sides * height and this can also be applied to rhombi and parallelograms.

There are slightly more complex formulae for regular polygons with 5 or more sides.

For even 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.