Comparing Areas and Perimeters (A) | Fun and Engaging 3rd Grade ... - Free Printable

Problem Overview:

The task involves comparing the perimeters of five different shapes (A, B, C, D, and E) drawn on a 1-inch square grid. Each shape is made up of 5 squares, so they all have the same area of \(5 \text{ in}^2\). The goal is to calculate the perimeter of each shape and identify which shape has a perimeter different from the others.

Step-by-Step Solution:

#### Shape A:
- Description: The shape is L-shaped.
- Perimeter Calculation:
- Count the number of outer edges of the shape.
- The shape has 10 outer edges.
- Therefore, the perimeter is \(10 \text{ in}\).

#### Shape B:
- Description: The shape is a cross.
- Perimeter Calculation:
- Count the number of outer edges of the shape.
- The shape has 12 outer edges.
- Therefore, the perimeter is \(12 \text{ in}\).

#### Shape C:
- Description: The shape is a T-shape.
- Perimeter Calculation:
- Count the number of outer edges of the shape.
- The shape has 10 outer edges.
- Therefore, the perimeter is \(10 \text{ in}\).

#### Shape D:
- Description: The shape is a straight line of 5 squares.
- Perimeter Calculation:
- Count the number of outer edges of the shape.
- The shape has 10 outer edges.
- Therefore, the perimeter is \(10 \text{ in}\).

#### Shape E:
- Description: The shape is an irregular shape with a protrusion.
- Perimeter Calculation:
- Count the number of outer edges of the shape.
- The shape has 12 outer edges.
- Therefore, the perimeter is \(12 \text{ in}\).

Comparison of Perimeters:

- Shape A: \(10 \text{ in}\)
- Shape B: \(12 \text{ in}\)
- Shape C: \(10 \text{ in}\)
- Shape D: \(10 \text{ in}\)
- Shape E: \(12 \text{ in}\)

Identifying the Shape with a Different Perimeter:

- Shapes A, C, and D all have a perimeter of \(10 \text{ in}\).
- Shapes B and E both have a perimeter of \(12 \text{ in}\).

Thus, the shapes with a perimeter different from the others are B and E. However, since the question asks for "which shape has a perimeter different to the others," we can conclude that Shape B or Shape E is the answer, as they stand out from the group of shapes with a perimeter of \(10 \text{ in}\).

Final Answer:

\[
\boxed{B}
\] or \(\boxed{E}\) (either one is correct based on the phrasing of the question).