Let's solve the problem step by step. The image contains three distinct figures labeled A, B, and C on a grid, and we're asked to find the total area of these figures, knowing that each square in the grid has a side length of 7 cm.

Step 1: Count the squares for each figure

• Figure A: Appears to be a house-like shape, consisting of a triangle and a square. By counting the squares:

  • There are 4 full squares in the base.
  • The triangle on top forms a right-angled triangle that is half the size of a square.

• Figure B: Appears to be a rectangle composed of 4 full squares.

• Figure C: Is a hexagonal-like figure, made up of a combination of a rectangle and two triangle shapes:

  • The rectangle fills 4 squares.
  • The two triangles together are equivalent to 1 full square (each triangle is half a square).

Step 2: Calculate the total area in terms of the grid

Each square represents $7 \, \text{cm} \times 7 \, \text{cm} = 49 \, \text{cm}^2$.

• Area of A:

  • 4 full squares = $4 \times 49 = 196 \, \text{cm}^2$
  • The triangle (half square) = $\frac{49}{2} = 24.5 \, \text{cm}^2$
  • Total area of A = $196 + 24.5 = 220.5 \, \text{cm}^2$

• Area of B:

  • 4 full squares = $4 \times 49 = 196 \, \text{cm}^2$

• Area of C:

  • 4 full squares = $4 \times 49 = 196 \, \text{cm}^2$
  • The two triangles together (1 full square) = $49 \, \text{cm}^2$
  • Total area of C = $196 + 49 = 245 \, \text{cm}^2$

Step 3: Total area of the three figures

Now, sum the areas of A, B, and C: $220.5 + 196 + 245 = 661.5 \, \text{cm}^2$

Thus, the total area of the figures A, B, and C is 661.5 cm².

Would you like further clarification or details on this?

Here are some related questions to explore further:

1. How do we calculate the area of irregular shapes using grid squares?
2. What is the area formula for a triangle, and how did it apply to figure A?
3. How can we use symmetry to simplify area calculations for geometric figures like C?
4. Why is it important to convert the side length into the area using square units?
5. How could the grid method be useful in estimating areas in real-world applications?

Tip: Always double-check that you've accounted for any partial squares, especially in composite figures like triangles.