To solve the problem, let's calculate the areas of the original and reduced triangles using the given information:
1. Calculating the area of the original triangle:
The original triangle has a base of 4 cm and a height of 8 cm. The area of a triangle is given by the formula: Area = (base * height) / 2.
Using this formula, we can calculate the area of the original triangle as follows:
Area_original = (4 cm * 8 cm) / 2
Area_original = 32 cm²
2. Calculating the area of the reduced triangle:
The triangle is being reduced by a ratio of 1:2, which means the base and height of the reduced triangle will be half of the original triangle's dimensions.
Base_reduced = 4 cm / 2
Base_reduced = 2 cm
Height_reduced = 8 cm / 2
Height_reduced = 4 cm
Using the same formula for the area of a triangle, we can calculate the area of the reduced triangle:
Area_reduced = (2 cm * 4 cm) / 2
Area_reduced = 4 cm²
3. Calculating the ratio by which the area of the triangle has been reduced:
The original triangle had an area of 32 cm², and the reduced triangle has an area of 4 cm². To find the reduction ratio, we divide the area of the reduced triangle by the area of the original triangle:
Reduction ratio = Area_reduced / Area_original
Reduction ratio = 4 cm² / 32 cm²
Reduction ratio = 1/8
So, the area of the original triangle is 32 cm², the area of the reduced triangle is 4 cm², and the area of the triangle has been reduced by a ratio of 1:8.