Question

Calculate the area of the irregular polygon shown below

Answer 1

Your answer: a)24 square inches

Answer 2

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)