Answer:
The area of the polygon is 42[tex]cm^{2}[/tex].
Step-by-step 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[tex]cm^{2}[/tex]
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[tex]cm^{2}[/tex]
Area of polygon = 144 - 102
= 42[tex]cm^{2}[/tex]
The area of the polygon is 42[tex]cm^{2}[/tex].
