Final answer:
The area of the larger triangle is twice the area of the smaller triangle. The total area for both triangles is 12 cm^2.
Step-by-step explanation:
To find the area of each triangle, we can use the formula for the area of a triangle, which is 1/2 × base × height. Since the two triangles are similar, they have the same shape and their corresponding sides are proportional. This means that the ratio of corresponding side lengths in the triangles is the same.
Let's compare the corresponding side lengths:
AB = 8 cm and BC = 4 cm. The ratio of AB to BC is 8:4 or 2:1.
Since the ratio of corresponding side lengths is 2:1, we can conclude that the ratio of the areas of the triangles is also 2:1. Therefore, the area of the larger triangle is twice the area of the smaller triangle.
To find the area of the smaller triangle, we can use the formula:
Area = 1/2 × base × height = 1/2 × 4 cm × 3 cm = 6 cm^2
The area of the larger triangle is twice the area of the smaller triangle, so the total area for both triangles is 2 × 6 cm^2 = 12 cm^2. Therefore, option D is correct.