Question

drag the yellow point until an accurate \height\ of the triangle is drawn. afterwards, fill out the empty boxes below to determine the area of the triangle.

Explanation:

Identify the base and height

Using the Right Triangle Geometry knowledge point, we must locate the correct altitude (height) of the triangle. An accurate height must be perpendicular to the chosen base. In the given diagram, the side of length \(6.1\) is perpendicular to the side of length \(6.6\), forming a right angle at the bottom-left vertex. Thus, we can choose:

• Base \(b = 6.6\)
• Height \(h = 6.1\)

Calculate the area

Using the Triangle Area Formula:

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

Substitute the values:

$$ \text{Area} = \frac{1}{2} \times 6.6 \times 6.1 = 3.3 \times 6.1 = 20.13 $$

Answer:

To find the area of the triangle, drag the yellow point to the bottom-left vertex so that the dashed line aligns with the perpendicular side of length \(6.1\), representing the true height \(h = 6.1\) perpendicular to the base \(b = 6.6\).

The area calculation is:

$$ \text{Area} = \frac{1}{2} \times 6.6 \times 6.1 = 20.13 $$