To find out how much greater the area of the original triangle is than the area of the dilated triangle, we first calculate the area of the original triangle.
The area \( A \) of a triangle is given by the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
For the original triangle:
- Base = 10 cm
- Height = 15 cm
Thus, the area of the original triangle is: \[ A_{\text{original}} = \frac{1}{2} \times 10 \times 15 = \frac{150}{2} = 75 \text{ cm}^2 \]
Next, we need to calculate the area of the dilated triangle. The scale factor for the dilation is \( \frac{4}{5} \). Therefore, the base and height of the dilated triangle will be:
- Dilated base = \( 10 \times \frac{4}{5} = 8 \) cm
- Dilated height = \( 15 \times \frac{4}{5} = 12 \) cm
Now we calculate the area of the dilated triangle: \[ A_{\text{dilated}} = \frac{1}{2} \times 8 \times 12 = \frac{96}{2} = 48 \text{ cm}^2 \]
Finally, we find the difference between the original area and the dilated area: \[ \text{Difference} = A_{\text{original}} - A_{\text{dilated}} = 75 \text{ cm}^2 - 48 \text{ cm}^2 = 27 \text{ cm}^2 \]
Thus, the area of the original triangle is greater than the area of the dilated triangle by \( \boxed{27} \) cm².
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