Calculate the area of the irregular polygon shown below
2 answers:
We divide the given figure into four parts as shown in the attachment
First we calculate the area of the three small rectangle that make up of the given figure. These small rectangles are named ABCD, EFGH and IJKL
Area of the rectangle ABCD = AB * AC
AC = 6 inches
AJ =MN = 12 inches
BE = 5 and FI = 5
AJ = AB+BE+EF+FI +IJ
12 = AB + 5+EF +5 + IJ
12-10 = AB + EF + IJ
AB + EF + IJ = 2
Since all the three segments are equal, AB = EF = IJ = 2/3
Area of rectangle ABCD = AB*AC = 2/3 * 6 = 4 square inches
Similarly area of rectangle EFGH = 4 square inches
Similarly area of rectangle IJKL = 4 square inches
Area of these small rectangles are named ABCD, EFGH and IJKL = 4 +4 +4 = 12 square inches
Now we have the area of the last big rectangle AMNJ = AM* MN
MN = 12 inches and AM = MC - AC = 7 - 6 = 1 inch
area of the last big rectangle AMNJ = 12 *1 = 12 square inches
Total area = area of small rectangles + area of big rectangle
Total area = 12 + 12 = 24 square inches (Option A)
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