We will solve different types of word problems on area and perimeter.
1. The perimeter of a rectangular field is 260 m. If its length is 90 m, find its breadth.
Solution:
Perimeter of a rectangle = 2(b + ℓ)
⟹ 260m = 2(b + 90 m)
⟹ 260 m = 2b + 180 m
⟹ (260 - 180) m = 2b
⟹ 80 m = 2b
⟹ 2b = 80 m
⟹ b = \(\frac{80}{2}\) m
⟹ b = 40 m
Hence, the breadth of the rectangular field = 40 m
2. Find the cost of fencing a square park of side 250 m at the rate of $ 20 per metre.
Solution:
Side of the park = 250 m
To calculate the cost of fencing, we require perimeter.
Perimeter of the square = 4 × one side
= 4 × 250 m
= 1000 m
Now, the total cost of fencing the park = $ 20 × 1000 = $ 20000
3. The side of a square plot of land is 35 m. Find the cost of levelling the plot, if the rate is $ 4 per square metre.
Solution:
Area of square = side × side
= 35 m × 35 m
= 1225 cm²
Levelling cost of 1 m² = $ 4
Levelling cost of 1225 m² = $ (4 × 1225)
= $ 4900
4. How many tiles, each measuring 2 m by 1 m, are required to cover a rectangular hall 12 m long and 8 m broad? Find the cost of tiles at $ 25 per tile.
Solution:
Length of a tile = 2 m
Breadth of a tile = 1 m
Therefore, Area of each tile = 2 m × 1 m
= 2 m²
Length of rectangular hall = 12 m
Breadth of rectangular hall = 8 m
Area of the hall = 12 m × 8 m
= 96 m²
Hence, number of tiles required
= \(\frac{\textrm{Area of the hall}}{\textrm{Area of one tile}}\)
= \(\frac{96}{2}\)
Therefore, Cost of tiles 48 × $ 25 = $ 1200
1. The sides of a triangular field are 20 cm, 15 cm, and 12 cm. Find the total distance travelled by a boy in taking 2 complete rounds of this field.
Answer:
1. 94 cm
2. The length and breadth of a rectangular park are 615 m and 550 m, respectively. Find the cost of fencing the park at the rate of $ 9.25 per metre.
Answer:
2. $ 21552.5
3. The length of a piece of wire is 78 m. If the wire is used to make a regular pentagon and a regular hexagon, find the difference in the lengths of its sides.
Answer:
3. 15.6 m - 13 m = 2.6 m
4. Find the length of a side of an equilateral triangle whose perimeter is 3 m 12 cm.
Answer:
4. 1.04 m
5. Stephen takes 2 rounds of a square park of side 135 m and Olivia takes 3 rounds of a rectangular park of length 70 m and breadth 45 m. Who covers more distance and by how much?
Answer:
5. Stephen; 390 m
6. Find the length of a rectangular park whose area is 204 sq m and breadth is 12 m.
Answer:
6. Length of a rectangular park = 17 m
7. The perimeter of a rectangular park is 270 m. If its length is 75 m, what will be its breadth?
Also calculate the area of this rectangular park.
Answer:
7. breadth = 60 m
Area of the rectangular park = 4500 m²
8. Find the area of a square if the length of its sides is doubled. Also, find the ratio of new area to its previous area.
Answer:
8. Area of the new square becomes 4 times when side is doubled.
Ratio of new area to its previous area = 4 : 1.
9. Two rectangles of length ℓ and breadth b are placed side by side along the length without any gap. Find the area of the new rectangle thus formed.
Answer:
9. Area of the new rectangle = 2ℓ × b = 2ℓb
10. The floor of a hall is completely covered by 25 carpets, each measuring 40 m × 2.5 m. What is the area of the floor?
Answer:
10. Area of the floor = 2500 m²
5th Grade Math Problems
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