Area of a polygon can be derived from sum of area of its sub-parts. The area of the considered polygon is given by: Option C: 316 cm²
Some polygon are of standard shapes like rectangle, triangle, parallelogram etc, but some are not standard and can be of any shape. For finding their area, we divide that non-standard polygon in parts such that it gets divided in standard polygons.
Then, we get:
Area of non-standard polygon = sum of all standard polygons forming that initial polygon.
For the given case, dividing the polygon in the shapes whose area we know(which is called here as standard polygons), as shown in the figure attached below, we get:
Area of polygon = Sum of area of those composing parts.
Area of polygon = Area of upper triangle ABC + Area of bottom rectangle BDEF
Height of ABC triangle = height of polygon - height of rectangle
Height of ABC = 18 - 14 = 4 cm
Base of ABC = length of BC = length of BD - length of CD = 21-10 = 11 cm
Thus, area of ABC = [tex]\dfrac{1}{2} \times base \times height = \dfrac{1}{2} \times 4 \times 11 = 22 \: \rm cm^2[/tex]
Area of rectangle BDEF = length times width = [tex]14 \times 21 = 294\: \rm cm^2[/tex]
Thus, area of polygon = Area of ABC + Area of BDEF = 22 + 294 cm²
Area of polygon = 316 cm² (option C)
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