Here are the step-by-step solutions for each problem on the worksheet.
1. A square has an area of 36 square centimetres. How long is each side of the square?
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Step 1: Remember that the area of a square is calculated by multiplying the side length by itself ($Side \times Side = Area$).
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Step 2: We need to find a number that, when multiplied by itself, equals 36.
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Step 3: Let's check some numbers:
* $5 \times 5 = 25$ (Too small)
* $6 \times 6 = 36$ (Correct!)
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Conclusion: The side length is 6 cm.
2. Louise bought 80 meters of fencing... what is the largest area it can have?
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Step 1: The total amount of fencing is the perimeter, which is 80 meters.
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Step 2: To get the largest possible area for a rectangle with a fixed perimeter, the shape should be a square (where all sides are equal).
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Step 3: A square has 4 equal sides. Divide the total fencing by 4 to find the length of one side:
$$80 \div 4 = 20 \text{ meters}$$
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Step 4: Calculate the area by multiplying the side lengths:
$$20 \times 20 = 400$$
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Conclusion: The largest area is 400 square meters.
3. Jules has a rectangular garden that measures 10 feet by 12 feet... Will Jules's garden have enough space to plant 3 seed packets?
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Step 1: First, calculate the total area of Jules's garden:
$$10 \text{ feet} \times 12 \text{ feet} = 120 \text{ square feet}$$
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Step 2: Calculate how much space is needed for 3 seed packets. One packet needs 40 square feet:
$$3 \text{ packets} \times 40 \text{ sq ft/packet} = 120 \text{ square feet}$$
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Step 3: Compare the garden size to the needed space. The garden is 120 sq ft, and he needs exactly 120 sq ft.
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Conclusion: Yes, he has exactly enough space.
4. Mrs. Lewis planted vegetables in a rectangular garden that was 20 feet long and 45 feet wide... How many square feet are left for other vegetables?
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Step 1: Find the total area of the garden:
$$20 \times 45 = 900 \text{ square feet}$$
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Step 2: Find the fraction of the garden used so far. She used $\frac{1}{3}$ for brinjals and $\frac{1}{5}$ for potatoes. To add these fractions, find a common denominator (15):
* $\frac{1}{3} = \frac{5}{15}$
* $\frac{1}{5} = \frac{3}{15}$
* Total used: $\frac{5}{15} + \frac{3}{15} = \frac{8}{15}$
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Step 3: Find the fraction remaining. The whole garden is $\frac{15}{15}$:
$$\frac{15}{15} - \frac{8}{15} = \frac{7}{15} \text{ remaining}$$
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Step 4: Calculate the area of the remaining part:
$$\frac{7}{15} \times 900$$
First, divide 900 by 15: $900 \div 15 = 60$.
Then, multiply by 7: $60 \times 7 = 420$.
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Conclusion: There are 420 square feet left.
5. What is the length of a rectangle that has an area of 100 ft and a width of 5 ft?
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Step 1: The formula for area is $Length \times Width = Area$.
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Step 2: We know the Area (100) and the Width (5). We need to find the Length.
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Step 3: Divide the area by the width:
$$100 \div 5 = 20$$
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Conclusion: The length is 20 ft.
6. What is the area of a square that is 7.5 cm on each side?
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Step 1: Multiply the side length by itself to find the area:
$$7.5 \times 7.5$$
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Step 2: Calculation:
$$7.5 \times 7.5 = 56.25$$
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Conclusion: The area is 56.25 square cm.
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Final Answer:
1. 6 cm
2. 400 square meters
3. Yes
4. 420 square feet
5. 20 ft
6. 56.25 sq cm
Parent Tip: Review the logic above to help your child master the concept of area and perimeter worksheet grade 6.
