To find the area of the scale drawing of the triangle, we first need to calculate the area of the original triangle and then scale it down to the dimensions of the drawing.
The formula for the area of a triangle is:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
For the original triangle:
- Base = 8 inches
- Height = 5 inches
Calculating the area of the original triangle:
\[ \text{Area} = \frac{1}{2} \times 8 \times 5 = \frac{1}{2} \times 40 = 20 \text{ square inches} \]
Now we need to determine the scale factor for the height from the original triangle to the scale drawing. The height of the scale drawing is 2 inches compared to the original height of 5 inches.
Calculating the scale factor:
\[ \text{Scale Factor} = \frac{\text{Height of scale drawing}}{\text{Height of original triangle}} = \frac{2}{5} \]
Since the area of a shape scales with the square of the linear dimensions, the area of the scale drawing can be calculated by multiplying the original area by the square of the scale factor:
\[ \text{Area of scale drawing} = \text{Area of original triangle} \times \left(\frac{\text{scale factor}}{1}\right)^2 \] \[ \text{Area of scale drawing} = 20 \times \left(\frac{2}{5}\right)^2 = 20 \times \frac{4}{25} \] \[ \text{Area of scale drawing} = 20 \times 0.16 = 3.2 \text{ square inches} \]
Thus, the area of Crystal's scale drawing is 3.2 square inches.