You know that the area of a geometrical figure represents its *planar* *extent*. Calculating the areas of planar geometrical figures is an important practical problem. For example, in the construction of a house, the floor area has a crucial role. Farmers routinely have to deal with issues related to the areas of their lands. In building ultra-fast computers, designers have to fit a very high number of electronic components in extremely small chip areas. Clearly, area problems occur in a variety of situations.

We note the following important facts about areas:

- Two congruent figures will have the same area. This should be obvious, since two congruent figures can be exactly superimposed over each other.
- Two non-congruent figures can have the same area. In other words, if two figures have the same area, you cannot say that they are congruent. As a simple example, consider a rectangle with sides 8 cm and 2 cm, and a square with each side equal to 4 cm. Both of these non-congruent figures will have the same area.
- The area of a rectangle with length
*l*and width*w*is*A*=*l*×*w*:

i

4. In the case of a square with side *s*, the area will be *A* = *s* × *s* = *s*^{2}:

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