To calculate the area of the dotted purple triangle, we can use the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

From the image, we can see that:

• The base of the triangle is 4 cm.
• The height of the triangle is 7 cm.

Now, applying the formula:

$\text{Area} = \frac{1}{2} \times 4 \, \text{cm} \times 7 \, \text{cm}$ $\text{Area} = \frac{1}{2} \times 28 \, \text{cm}^2$ $\text{Area} = 14 \, \text{cm}^2$

So, the area of the dotted purple triangle is 14 cm².

Would you like any further details on this? Here are 5 related questions for deeper exploration:

1. How does the formula for the area of a triangle change if the triangle is not a right triangle?
2. Can you calculate the perimeter of the triangle given the base and height?
3. How would the area change if both the base and height were doubled?
4. How can you find the area of a triangle using trigonometry if you know two sides and the included angle?
5. What is the relation between the area of this triangle and the rectangle that encloses it?

Tip: For triangles, knowing the height and base is essential for using the standard area formula, but when dimensions are missing, other techniques like Heron's formula or trigonometry can be helpful.