Solved Exercises on Finding Perimeter of Rectangular Prism in Grade 3

Master finding perimeter of rectangular prisms: edge lengths, perimeter calculations, geometric properties through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic rectangular prism
Exercise 1
A rectangular prism has length 4 units, width 3 units, and height 2 units. What is the perimeter of its base?
Definition:

Rectangular Prism: A 3D shape with 6 rectangular faces, 12 edges, and 8 vertices

Base: The bottom face of the prism (a rectangle)

Perimeter of Base: The distance around the bottom rectangle

Perimeter method:
  1. Identify the base rectangle dimensions (length and width)
  2. Apply rectangle perimeter formula: P = 2(length + width)
Given
Length = 4, Width = 3
Formula
P = 2(l+w)
Result
P = 14
Step 1: Identify the base dimensions

For the base rectangle: length = 4 units, width = 3 units

The height (2 units) is not needed for the base perimeter

Step 2: Apply the perimeter formula

Perimeter = 2 × (length + width)

Perimeter = 2 × (4 + 3)

Step 3: Calculate the result

Perimeter = 2 × 7 = 14 units

Perimeter of base = 14 units
Final answer:

The perimeter of the base is 14 units

Applied rules:

• Rectangular Prism Property: The base is a rectangle with length and width

• Perimeter Formula: P = 2(l+w) for rectangles

• Dimension Focus: Only length and width matter for base perimeter

2 Different base dimensions
Exercise 2
A rectangular prism has length 6 units, width 5 units, and height 4 units. What is the perimeter of its base?
Definition:

Base Perimeter: The distance around the bottom rectangle of the prism

Top Face: Has the same perimeter as the base

Given
Length = 6, Width = 5
Formula
P = 2(l+w)
Result
P = 22
Step 1: Identify the base dimensions

Base rectangle: length = 6 units, width = 5 units

Height (4 units) doesn't affect the base perimeter

Step 2: Apply the perimeter formula

Perimeter = 2 × (length + width)

Perimeter = 2 × (6 + 5)

Step 3: Calculate the result

Perimeter = 2 × 11 = 22 units

Perimeter of base = 22 units
Final answer:

The perimeter of the base is 22 units

Applied rules:

• Rectangular Prism Property: Base and top are identical rectangles

• Perimeter Formula: P = 2(l+w)

• Height Irrelevance: Height doesn't affect base perimeter

3 Cube base perimeter
Exercise 3
A cube has all edges measuring 3 units. What is the perimeter of its base?
Definition:

Cube: A special rectangular prism where all edges are equal

Square Base: All sides of the base are equal

Given
All edges = 3 units
Square
P = 4s
Result
P = 12
Step 1: Identify the base dimensions

Since it's a cube, the base is a square with all sides equal to 3 units

Length = 3 units, Width = 3 units

Step 2: Apply the perimeter formula

Method 1: P = 2(l + w) = 2(3 + 3) = 2(6) = 12

Method 2: P = 4s = 4(3) = 12 (since it's a square)

Step 3: Calculate the result

Perimeter = 12 units

Step 4: Verify with rectangle formula

P = 2(l + w) = 2(3 + 3) = 2(6) = 12 ✓

Perimeter of base = 12 units
Final answer:

The perimeter of the base is 12 units

Applied rules:

• Cube Property: All edges are equal

• Square Perimeter: P = 4s where s is the side length

• Rectangle Perimeter: P = 2(l+w) also works for squares

Rules and methods, laws,...
\(P_{base} = 2(l + w)\)
Perimeter of Rectangular Prism Base
Rectangular Prism
\(12 \text{ edges}, 6 \text{ faces}\)
Properties
Base Perimeter
\(P = 2(l + w)\)
Rectangle formula
Cube Base
\(P = 4s\)
When all sides equal
Key definitions:

Rectangular Prism: A 3D shape with 6 rectangular faces, 12 edges, and 8 vertices

Base: The bottom face of the prism (always a rectangle)

Perimeter: The total distance around the outside of a shape

Edge: A line segment where two faces meet

Complete methodology:
  1. Identify the shape: Confirm it's a rectangular prism
  2. Locate the base: Identify the bottom rectangular face
  3. Measure dimensions: Find the length and width of the base
  4. Apply formula: Use P = 2(l + w) for the base perimeter
  5. Calculate: Perform the arithmetic
Tip 1: The base of a rectangular prism is always a rectangle.
Tip 2: The height of the prism doesn't affect the base perimeter.
Tip 3: The top face has the same perimeter as the base.
Tip 4: A cube is a special rectangular prism where all edges are equal.
Common errors: Including height in perimeter calculation, confusing perimeter with area, mixing up length and width.
Memory aids: "Perimeter is the fence around the yard" and "Only length and width matter for the base".
Formulas to know by heart:

• Perimeter of rectangle: P = 2(l + w)

• Perimeter of square: P = 4s

• Area of rectangle: A = l × w

• Volume of rectangular prism: V = l × w × h

Solution: Exercises 4 to 5
4 Real-world application
Exercise 4
A shoebox shaped like a rectangular prism has a length of 8 inches and a width of 5 inches. What is the perimeter of the base of the box?
Definition:

Real-world application: Connecting math to everyday objects

Shoebox model: A common example of a rectangular prism

Given
Length = 8 in, Width = 5 in
Formula
P = 2(l+w)
Result
P = 26 in
Step 1: Identify the base dimensions

The base of the shoebox is a rectangle with length = 8 inches and width = 5 inches

The height of the box is not given and not needed for the base perimeter

Step 2: Apply the perimeter formula

Perimeter = 2 × (length + width)

Perimeter = 2 × (8 + 5)

Step 3: Calculate the result

Perimeter = 2 × 13 = 26 inches

Step 4: Include units

Always include the unit of measurement in your answer

Perimeter of base = 26 inches
Final answer:

The perimeter of the base of the shoebox is 26 inches

Applied rules:

• Real-world modeling: Representing physical objects with geometric shapes

• Unit awareness: Including measurement units in the final answer

• Relevant dimensions: Identifying which measurements are needed

5 Comparison problem
Exercise 5
Box A is a rectangular prism with length 7 cm, width 4 cm. Box B is a cube with all edges 5 cm. Which box has a larger base perimeter?
Definition:

Comparison problem: Calculating and comparing measurements

Rectangular vs Square base: Different formulas but same concept

Box A
P = 2(7+4) = 22cm
Box B
P = 4×5 = 20cm
Result
Box A > Box B
Step 1: Calculate Box A's base perimeter

Box A is a rectangular prism with length = 7 cm, width = 4 cm

Perimeter of base = 2 × (length + width) = 2 × (7 + 4) = 2 × 11 = 22 cm

Step 2: Calculate Box B's base perimeter

Box B is a cube with all edges = 5 cm

The base is a square with side length = 5 cm

Perimeter of base = 4 × side = 4 × 5 = 20 cm

Step 3: Compare the perimeters

Box A: 22 cm

Box B: 20 cm

22 cm > 20 cm

Step 4: State the conclusion

Box A has a larger base perimeter than Box B

Box A has the larger base perimeter (22 cm vs 20 cm)
Final answer:

Box A has a larger base perimeter (22 cm) than Box B (20 cm)

Applied rules:

• Comparison strategy: Calculate both values before comparing

• Different shapes: Apply appropriate formulas for each shape

• Units consistency: Both measurements in the same unit

Complete Guide: Laws, Methods, Rules, Definitions, Expressions
\(P_{base} = 2(l + w)\)
Perimeter of Rectangular Prism Base
Key definitions:

Rectangular Prism: A 3D shape with 6 rectangular faces, 12 edges, and 8 vertices. Also called a cuboid.

Base: The bottom face of the prism, which is always a rectangle. The top face is identical to the base.

Perimeter: The total distance around the outside edge of a 2D shape.

Edge: A line segment where two faces of the prism meet.

Face: A flat surface of the prism (all are rectangles in a rectangular prism).

Complete methodology:
  1. Identify the shape: Confirm you're working with a rectangular prism
  2. Locate the base: Identify which face is considered the base (usually the bottom)
  3. Extract dimensions: Find the length and width of the base rectangle
  4. Select formula: Use P = 2(l + w) for the rectangular base
  5. Calculate: Substitute values and perform arithmetic
  6. Verify: Check that the answer makes sense in context
Tip 1: Always identify which dimensions belong to the base. The height of the prism is not part of the base perimeter.
Tip 2: A cube is a special rectangular prism where length = width = height.
Tip 3: The base and top faces of a rectangular prism have identical perimeters.
Tip 4: Remember to include units in your final answer.
Rectangular Prism Properties: 6 rectangular faces, 12 edges, 8 vertices, opposite faces are identical.
Base Characteristics: Always rectangular, shares length and width with the rectangular prism.
Common Errors: Including height in perimeter calculation, confusing perimeter with area or volume.
Essential formulas:

• Perimeter of rectangle: P = 2(l + w)

• Perimeter of square: P = 4s

• Area of rectangle: A = l × w

• Volume of rectangular prism: V = l × w × h

• Surface area of rectangular prism: SA = 2(lw + lh + wh)

Rectangular Prism Perimeter Infographic
📦
Prism Structure

• 6 rectangular faces

• 12 edges

• 8 vertices

• Base = Top (identical)

Base Perimeter

• P = 2(l + w)

• Only length & width matter

• Height is irrelevant

• Units: same as edge lengths

Special Cases

• Cube: P = 4s

• Square base: P = 4s

• Rectangle base: P = 2(l+w)

• Same formula for top & bottom

Problem-Solving Workflow
1
Identify Shape
2
Locate Base
3
Get Dimensions
4
Apply Formula
5
Calculate & Check
Visual Representation

Rectangular prism with length (l), width (w), height (h)

Base is rectangle: perimeter = 2(l + w)

Top face has same perimeter as base

Remember: Base perimeter only uses length and width, not height!

Questions & Answers

Question: What's the difference between the perimeter of a rectangular prism and the perimeter of its base? Isn't the perimeter the whole shape?

Answer: Great question! There's an important distinction here:

  • Perimeter of the base: This is the distance around the bottom rectangle of the prism. It's calculated as P = 2(length + width).
  • Total edge length of the prism: This would be the sum of all 12 edges of the 3D shape, which is 4(length) + 4(width) + 4(height).

In grade 3, when we talk about "perimeter of a rectangular prism," we usually mean the perimeter of its base (the bottom rectangle). The base is a 2D shape (rectangle), so we can find its perimeter using the rectangle formula.

Think of it this way: if you traced around the bottom of a shoebox, that's the perimeter of the base. The prism itself is 3D, so it doesn't have a traditional perimeter like a 2D shape does.

Question: Does the height of the rectangular prism affect the perimeter of the base?

Answer: No, the height of the rectangular prism does NOT affect the perimeter of the base. Here's why:

  • The base is the bottom rectangle of the prism, defined only by its length and width
  • Height is the measurement going up from the base, perpendicular to the base
  • Perimeter of the base = 2(length + width), which doesn't include height

Think of it like this: if you have a tall box or a short box with the same bottom dimensions, the distance around the bottom edge (the perimeter of the base) is the same for both boxes.

For example, a box that's 4 units long, 3 units wide, and 10 units tall has the same base perimeter as a box that's 4 units long, 3 units wide, and 2 units tall. Both have a base perimeter of 2(4+3) = 14 units.

Question: Is the perimeter of the top of the rectangular prism the same as the perimeter of the base?

Answer: Yes, the perimeter of the top of a rectangular prism is exactly the same as the perimeter of the base! Here's why:

  • A rectangular prism has two parallel, identical rectangular faces: the top and the bottom (base)
  • Both the top and base have the same length and width dimensions
  • Since perimeter depends only on length and width, both have the same perimeter

In fact, if you look at a rectangular prism, the top face and the base face are congruent rectangles (same size and shape). They have identical dimensions: the same length and the same width.

So if the base has a perimeter of 2(l + w), then the top also has a perimeter of 2(l + w). They're mirror images of each other, just separated by the height of the prism.