To find the area of Crystal's scale drawing of the triangle, we first need to calculate the area of the original triangle using the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
For the original triangle:
- Base = 8 inches
- Height = 5 inches
Calculating the area:
\[ \text{Area} = \frac{1}{2} \times 8 \times 5 = \frac{1}{2} \times 40 = 20 \text{ square inches} \]
Next, we need to determine the scale of the drawing. The height of the original triangle is 5 inches and the height of the scale drawing is 2 inches.
To find the scale factor, we divide the height of the scale drawing by the height of the original triangle:
\[ \text{Scale factor} = \frac{\text{Height of scale drawing}}{\text{Height of original triangle}} = \frac{2}{5} \]
Now, we can use the square of the scale factor to find the area scaling factor since area changes with the square of the linear dimensions:
\[ \text{Area scaling factor} = \left(\frac{2}{5}\right)^2 = \frac{4}{25} \]
Now we can calculate the area of the scale drawing:
\[ \text{Area of scale drawing} = \text{Area of original triangle} \times \text{Area scaling factor} = 20 \times \frac{4}{25} \]
Calculating this gives:
\[ \text{Area of scale drawing} = 20 \times \frac{4}{25} = \frac{80}{25} = 3.2 \text{ square inches} \]
Therefore, the area of Crystal's scale drawing is:
3.2 square inches.
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