To solve this problem, we need to ensure the area of the parallelogram equals the area of the triangle.

Step 1: Area of the Triangle

The formula for the area of a triangle is: $\text{Area of Triangle} = \frac{1}{2} \times \text{base} \times \text{height}$ For the triangle:

• Base = 6 cm
• Height = 4 cm

$\text{Area of Triangle} = \frac{1}{2} \times 6 \times 4 = 12 \, \text{cm}^2$

Step 2: Area of the Parallelogram

The formula for the area of a parallelogram is: $\text{Area of Parallelogram} = \text{base} \times \text{height}$ For the parallelogram:

• Height = 3 cm
• Base = $x$ (the missing number)

Since the areas of the parallelogram and triangle are the same: $\text{Area of Parallelogram} = 12 \, \text{cm}^2$ Substitute into the formula: $x \times 3 = 12$ Solve for $x$: $x = \frac{12}{3} = 4$

Final Answer:

The number that should go in the box is 4.

Would you like further explanation or details?

Related Questions:

1. How is the formula for the area of a triangle derived?
2. Why does the parallelogram formula not require dividing by 2?
3. Can you explain the difference between base and height in geometric areas?
4. What happens if we change the height of the parallelogram to 4 cm? How would the base change?
5. How are area formulas used in real-world applications?

Tip:

Always match units carefully in geometry problems to avoid mistakes.