💡 3rd Grade Math: Area and Perimeter Practice Questions

📌 The perimeter is the total distance around the outside of a shape. For a rectangle, you add up the lengths of all four sides.

• 👉 A rectangle has two long sides (length) and two short sides (width).
• 👉 Length = 10 inches
• 👉 Width = 6 inches
• 💡 We add: Length + Width + Length + Width
• \[ \text{Perimeter} = 10 \text{ inches} + 6 \text{ inches} + 10 \text{ inches} + 6 \text{ inches} \]
• \[ \text{Perimeter} = 32 \text{ inches} \]

✅ The perimeter of the photo frame is 32 inches.

📌 A square is a special type of rectangle where all four sides are the same length.

• 👉 Each side of the square painting is 5 feet.
• 💡 To find the perimeter, we add the length of all four sides.
• \[ \text{Perimeter} = 5 \text{ feet} + 5 \text{ feet} + 5 \text{ feet} + 5 \text{ feet} \]
• \[ \text{Perimeter} = 20 \text{ feet} \]

✅ The perimeter of the painting is 20 feet.

📌 The area is the amount of space inside a flat shape. For a rectangle, you multiply its length by its width.

• 👉 Length of the kitchen floor = 8 feet
• 👉 Width of the kitchen floor = 7 feet
• 💡 To find the area, we multiply Length \(\times\) Width.
• \[ \text{Area} = 8 \text{ feet} \times 7 \text{ feet} \]
• \[ \text{Area} = 56 \text{ square feet} \]

✅ Mr. Chen needs 56 square feet of tiles to cover his kitchen floor.

📌 Remember, a square has all sides equal. To find the area of a square, you multiply the side length by itself.

• 👉 Side length of the sandbox = 9 meters
• 💡 To find the area, we multiply Side \(\times\) Side.
• \[ \text{Area} = 9 \text{ meters} \times 9 \text{ meters} \]
• \[ \text{Area} = 81 \text{ square meters} \]

✅ The area of the sandbox is 81 square meters.

📌 We know the total perimeter and the length of one side. We need to find the missing width.

• 👉 Total Perimeter = 24 inches
• 👉 Length = 7 inches
• 💡 In a rectangle, opposite sides are equal. So, there are two sides of 7 inches each.
• 👉 Sum of the two lengths = \( 7 \text{ inches} + 7 \text{ inches} = 14 \text{ inches} \)
• 💡 Now, subtract the sum of the lengths from the total perimeter to find the sum of the two widths.
• 👉 Sum of the two widths = \( 24 \text{ inches} - 14 \text{ inches} = 10 \text{ inches} \)
• 💡 Since there are two widths, and they are equal, divide the sum by 2.
• 👉 Width = \( 10 \text{ inches} \div 2 = 5 \text{ inches} \)

✅ The width of the picture frame is 5 inches.

📌 To compare which garden is larger, we need to find the area of each garden first.

For Garden A:

• 👉 Length = 4 feet, Width = 5 feet
• 💡 Area of Garden A = Length \(\times\) Width
• \[ \text{Area A} = 4 \text{ feet} \times 5 \text{ feet} = 20 \text{ square feet} \]

For Garden B:

• 👉 Length = 3 feet, Width = 7 feet
• 💡 Area of Garden B = Length \(\times\) Width
• \[ \text{Area B} = 3 \text{ feet} \times 7 \text{ feet} = 21 \text{ square feet} \]

Compare the areas:

• 👉 Area A = 20 square feet
• 👉 Area B = 21 square feet
• 💡 Since \( 21 > 20 \), Garden B has a larger area.

✅ Garden B has a larger area.

📌 This is a real-world problem about perimeter because Maria needs to know the total length of the boundary to buy enough fencing material.

• 👉 Length of the fenced area = 9 meters
• 👉 Width of the fenced area = 4 meters
• 💡 To find the amount of fencing material, we calculate the perimeter.
• \[ \text{Perimeter} = 9 \text{ meters} + 4 \text{ meters} + 9 \text{ meters} + 4 \text{ meters} \]
• \[ \text{Perimeter} = 26 \text{ meters} \]

✅ Maria needs to buy 26 meters of fencing material.

📌 This is a real-world problem about area because the baker needs to know the total surface space of the cake top to cover it with frosting.

• 👉 Length of the cake top = 12 inches
• 👉 Width of the cake top = 8 inches
• 💡 To find the total area to cover, we multiply the length by the width.
• \[ \text{Area} = 12 \text{ inches} \times 8 \text{ inches} \]
• \[ \text{Area} = 96 \text{ square inches} \]

✅ The baker needs to cover a total area of 96 square inches with frosting.