To help you solve this problem, let’s analyze each part and fill in the blanks with calculations based on the image.

1. Area of the Two Small Triangles:

Each small triangle has a base and height of $x + 3$.

The area of a single triangle is calculated using: $A = \frac{\text{base} \times \text{height}}{2}$ Thus, the area of one triangle is: $A = \frac{(x+3)(x+3)}{2}$ The area of two such triangles would be: $A_{\text{two triangles}} = 2 \times \frac{(x+3)(x+3)}{2} = (x+3)^2$

2. Area of the Square:

The side of the square is also $x + 3$, so the area of the square is: $A_{\text{square}} = (x+3)(x+3) = (x+3)^2$

3. Area of the Large Triangle:

The large triangle has a base of $2x + 6$ and a height of $2x + 6$.

Using the area formula for a triangle: $A_{\text{large triangle}} = \frac{\text{base} \times \text{height}}{2} = \frac{(2x+6)(2x+6)}{2}$

Summary of Areas

• Area of Two Small Triangles: $(x+3)^2$
• Area of the Square: $(x+3)^2$
• Area of the Large Triangle: $\frac{(2x+6)^2}{2}$

Would you like to proceed with further simplification or verification of these areas?

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Here are five related questions to further explore:

1. How can we simplify $(x+3)^2$ to get a clearer expression?
2. What is the expanded form of $(2x+6)^2$ to fully simplify the area of the large triangle?
3. Can we use these area expressions to find a relationship between $x$ and the areas?
4. What happens to the area of each shape if $x$ is doubled?
5. How do these formulas change if the base and height are not equal?

Tip: When dealing with expressions like $(a + b)^2$, remember to expand them as $a^2 + 2ab + b^2$ to simplify calculations.