Composite figures can be subdivided into standard shapes. The area of the considered composite shape is 112 sq. cm
Area of some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc is already derived.
When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.
Thus, we have:
[tex]\text{Area of composite figure} = \sum (\text{Area of composing figures})[/tex]
That ∑ sign shows "sum"
The missing image is attached below.
We can split this composite figure in two parts by extending the line CG to meed AE on the point D. It makes a square (top) and a rectangle(bottom) as shown in the right sided image.
Area of the figure = Area of the top square + Area of the bottom rectangle.
Length of AE = |AE| = 16 cm
|AE| = |AD| + |DE| = 16
|DE| = |GF| = 8 cm
Thus, we get:
|AD| + 8 = 16
|AD| = 8 cm
Assuming the sides AD and BC are parallel, and so as the pair of sides AC and BD, and adjacent sides are perpendicular, its a rectangle with length = width = 8 cm, so its a square of side length 8 inches.
Area of square ABCD of side length 8 inches = [tex]\rm side^2 = 8^2 = 16 \: cm^2[/tex]
Assuming opposite sides of DEFG are parallel to each other and adjacent ones are perpendicular, we get:
|DE| = |GF| = 8 cm
|EF| = |DG| = |DC| + |CG| = |AB| + |CG| = 8+8 = 16 inches
Thus, its a rectagle with dimensions of 8 cm by 16 cm.
Thus, its area is: [tex]\rm Length \times width = 8 \times 12 = 96 \: \rm cm^2[/tex]
Thus, area of the composite figure = 16 + 96 = 112 sq. cm.
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