area and perimeter---**Extraction Content:**
**Title:**
AREA AND PERIMETER
**Introduction:**
1. These figures are made up of 1cm squares
**Figures Description:**
The image shows three figures, labeled A, B, and C, each composed of 1cm squares arranged in different shapes. Grid lines indicate the boundaries of the 1cm squares.
* Figure A: This figure is light green. It is composed of 6 squares arranged in an irregular shape.
* Figure B: This figure is light purple/blue. It is composed of 7 squares arranged in a stepped shape with a single square at the bottom connected to the center of a horizontal row of three squares, with another horizontal row of three squares on top.
* Figure C: This figure is light pink. It is composed of 7 squares arranged in a shape resembling a plus sign with two squares attached horizontally to the top arm and one square attached to the bottom arm.
**Calculations (derived from description, not explicitly in image but needed to answer questions):**
* Figure A: Area = 6 squares * 1 cm²/square = 6 cm². Perimeter = 10 cm (by counting exposed edges).
* Figure B: Area = 7 squares * 1 cm²/square = 7 cm². Perimeter = 11 cm (by counting exposed edges).
* Figure C: Area = 7 squares * 1 cm²/square = 7 cm². Perimeter = 11 cm (by counting exposed edges).
**Questions:**
a. Which two figures have the same area?
b. Which two figures have the same perimeter?
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Welcome to our lesson on area and perimeter. Today we'll work with three figures made of one centimeter squares. Figure A is green and has six squares. Figure B is blue and has seven squares arranged in a stepped pattern. Figure C is pink and also has seven squares arranged in a plus-like shape. We'll calculate their areas and perimeters to compare them.
Now let's calculate the area of each figure. Area equals the number of squares. Figure A has six squares, so its area is six square centimeters. Figure B has seven squares, giving it an area of seven square centimeters. Figure C also has seven squares, so it also has an area of seven square centimeters. This means figures B and C have the same area.
Now let's calculate the perimeter of each figure. Perimeter is the total length of all exposed edges. For Figure A, we count ten exposed edges, giving a perimeter of ten centimeters. Figure B has eleven exposed edges, so its perimeter is eleven centimeters. Figure C also has eleven exposed edges, making its perimeter eleven centimeters as well. Therefore, figures B and C have the same perimeter.
Let's now answer the questions. Question A asks which two figures have the same area. The answer is figures B and C, both with seven square centimeters. Question B asks which two figures have the same perimeter. Again, the answer is figures B and C, both with eleven centimeters. Even though these figures have different shapes, they share the same area and perimeter measurements.
To summarize what we have learned today: Area is calculated by counting the number of unit squares in a figure. Perimeter is found by measuring the total length of all exposed edges. Different shaped figures can have identical area and perimeter measurements. In our example, figures B and C shared both the same area of seven square centimeters and the same perimeter of eleven centimeters, demonstrating that shape does not determine these measurements.