Practice the questions given in the worksheet on area of the path. Students can recall the topic and practice the questions to get more idea how to find area of the path.
1. A verandah 1.25 m is constructed all along outside of a room 7.5 m long and 5 m wide.
(a) the area of the verandah.
(b) the cost of cementing the floor of the verandah at the rate of $15 per m².
2. A floor is 10 m long and 6 m wide. A square carpet of side 5 m is laid on the floor.
Find the area of the floor not carpeted.
3. Four square flowerbeds each of sides 2 m are dug on a piece of land 12 m long and 9 m wide. Find the area of the remaining portion of the land. Find the cost of levelling this land at the rate of $3 per 100 cm².
4. The side of a square flowerbed is 1 m 60 cm. It is enlarged by digging a path 25 cm wide all around.
(a) the increase in the area of flowerbed.
(b) the area of the enlarged flowerbed.
5. Two crossroads, each of width 8 m, run at right angles through the centre of a rectangular garden of length 500 m and breadth 250 m and parallel to its sides.
(a) the area of the garden excluding crossroads.
(b) the area of the crossroads.
Convert these areas into hectares and ares.
6. A rectangular field is of dimensions 20 m × 15 m. Two paths run parallel to the sides of the rectangle through the centre of the field. The width of the longer path is 2 m and that of the shorter path is 1 m.
(a) area of the paths
(b) area of the remaining portion of the field.
(c) cost of constructing the roads at the rate of $10 per m².
7. A square lawn is surrounded by a path 2 m wide. If the area of the path is 240 m², find the area of the lawn.
8. A path 5 m wide runs along inside a rectangular field. The length of the rectangular field is three times the breadth of the field. If the area of the path is 500 m², then find the length and breadth of the field.
9. A strip of width 3 cm is cut out all round from a sheet of paper with dimensions 30 cm × 20 cm. Find the area of the strip cut out and the area of the remaining sheet.
Answers for worksheet on area of the path are given below to check the exact answers of the above questions.
1. (a) 37.5 m²
(b) $ 562.50
2. 35 m²
3. 92 m², $ 27600
4. 1.85 m², 4.41 m²
5. (a) 1190.64 ares or 11.9064 hectares
(b) 59.36 ares or 0.5936 hectares
6. (a) 53 m²
(b) 247 m²
7. 210.25 m²
8. L = 45 m, b = 15 m
9. 264 cm², 336 cm²
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