Question

Find the area of the missing piece of the polygon and explain your process for finding it:

Answer 1

The area of the polygon is 42
`cm^(2)`.

Explanation:

A polygon is a shape that has three or more sides. They are named with respect to the number of their sides. Example, an octagon has 8 sides, hexagon has 6 sides etc.

From the given figure, the area of the shaded polygon can be calculated by;

Area of polygon = Area of square - Sum of areas given

Sum of areas given = 24 + 30 + 48

= 102
`cm^(2)`

The four sides of the figure are equal, thus it is a square. The length of each side is 12 cm, so that:

Area of square = length × width

= 12 × 12

= 144
`cm^(2)`

Area of polygon = 144 - 102

= 42
`cm^(2)`

The area of the polygon is 42
`cm^(2)`.