Mathematics
A rectangular field is 30 m in length and 22 m in width. Two mutually perpendicular roads, each 2.5 m wide, are drawn inside the field so that one road is parallel to the length of the field and the other road is parallel to its width. Calculate the area of the crossroads.
Area Trapezium Polygon
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Answer
Given:
Length of the rectangular field = 30 m
Width of the rectangular field = 22 m
Width of each road = 2.5 m
Area of crossroad IJKL (parallel to the width of field) = 2.5 x 22 m2
= 55 m2
Area of crossroad EFGH (parallel to the length of field) = 2.5 x 30 m2
= 75 m2
Side of the square MNOP = 2.5
As we know, the area of the square = side2
Area of the square field MNOP (area common to both roads) = 2.52 m2
= 6.25 m2
Now, area of crossroad = Area of cross road EFGH + Area of cross road IJKL - Area of square field MNOP
= 75 m2 + 55 m2 - 6.25 m2
= 130 m2 - 6.25 m2
= 123.75 m2
Hence, the area of the crossroads is 123.75 m2.
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