The area of polygon given below in the image attached is 65 square units.
What is the area of a polygon?
For finding the area of a polygon which is not regular or its formula is not defined, we split the figure into triangles, squares, trapezium, etc. The purpose is to visualize the given geometry as a combination of geometries for which we know how to calculate the area. We then calculate the area for each of the part and then add them up to obtain the area of the polygon.
We need to figure out the area of polygon QRSTU.
As can be seen the image attached below, the polygon QRSTU can be written as:
QRATU = rectangle ABCR - ΔATS - ΔTBU - ΔQCU
Area of rectangle ABCR = length x breadth = 11 x 8 = 88 sq. units
Area of ΔATS = 1/2 x Base x Height = 1/2 x AT x AS = 1/2 x 4 x 4 = 8 sq. units
Area of ΔTBU = 1/2 x Base x Height = 1/2 x TB x BU = 1/2 x 4 x 4 = 8 sq. units
Area of ΔQCU = 1/2 x Base x Height = 1/2 x UC x QC = 1/2 x 7 x 2 = 7 sq. units
Area of polygon QRATU = (88 - 8 - 8 - 7) sq. units = 65 sq. units
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