Answer:
To find the area of the reduced triangle, we need to know the length of the base and the height of the triangle after the scaling.
Since the triangle has been reduced by a scale of 0.4, the length of each side has been multiplied by 0.4. Therefore, the base of the reduced triangle is:
10 cm × 0.4 = 4 cm
To find the height of the reduced triangle, we can use the fact that the ratio of corresponding sides in similar triangles is the same. Since the triangle has been scaled down by a factor of 0.4, the ratio of the corresponding sides is 0.4. Therefore, the height of the reduced triangle is:
30 cm × 0.4 = 12 cm
Now that we know the base and the height of the reduced triangle, we can calculate its area using the formula:
Area = (1/2) × base × height
Area = (1/2) × 4 cm × 12 cm
Area = 24 cm²
Therefore, the area of the reduced triangle is 24 cm².
Explanation: