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### Grade 7 - Mathematics9.44 Area of Rectangular Path - I

 Example: A path of 2 metres wide runs around out side a rectangular plot of length 25 metres and width 20 metres. Find the area of the path. Solution: Given that, The length (l) = 25 metres, width (b) = 20 metres and width of the path (w) = 2 metres. Since the path runs out side the rectangular plot, the measurements of the outer rectangle are (l+2w) and (b+2w) ie = 25 + (2*2) and 20 + (2*2) = 25+4 and 20+4 = 29 and 24 Hence the area of the outer rectangle = (l+2w)(b+2w) = 29 * 24 = 696 square metres. The area of the inner rectangle = l * b = 25 * 20 = 500 square metres. Area of the path = (The area of the outer rectangle) - (The area of the inner rectangle) i.e (l+2w)(b+2w) - lb = 696 - 500 = 196 square metres. Therefore, the area of the path is 196 square metres. Directions: Read the above example carefully and answer the following questions: Draw a rectangular plot of side 12 centi-metres and 15 centi-metres. Draw a path of width 2 centimetres, around and outside the rectangular plot. Find the area of the path. Use different colors to represent the path and the rectangular plot.
 Q 1: A path of 2.5 metres wide, runs around out side a rectangular plot of width 13 metres. Find the length of the rectangular plot if the area of the path is given by 111 square metres.18 metres2 metres94 metres74 metres Q 2: A path of 3 metres runs around out side a rectangular plot of length 26 metres and width 22 metres. Find the area of the path.125 square metres257 square metres324 square metres785 square metres Q 3: A path of 1 metre wide, runs around out side a rectangular plot of length 20 metres. Find the width of the rectangular plot if area of the path is given by 74 square metres10 metres5 metres15 metres9 metres Q 4: A path of 2 metres wide, runs around out side a rectangular plot of width 12 metres. Find the length of the rectangular plot if the area of the path is given by 124 square metres.14 metres15 metres13 metres12 metres Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!