Triangles ABC and DEF are similar. Find the area of triangle ABC. Round your answer to the nearest tenth.

Triangle ABC has a base of 12m.
Triangle DEF has a base of 18m and height of 12m

To find the area of triangle ABC, we need to know the height. However, the height of triangle ABC is not given in the question.

To find the area of triangle ABC, we can use the concept of similarity. Since triangles ABC and DEF are similar, their corresponding sides are in proportion.

First, we need to find the corresponding side of triangle ABC to triangle DEF. We can do this by setting up a proportion with the base lengths of the two triangles:

(AB / DE) = (BC / EF)

Substituting the given values, we have:

(12 / 18) = (BC / 12)

Now, we can solve for BC:

BC = (12 / 18) * 12
BC = 8

So, the length of side BC in triangle ABC is 8m.

Now that we have the base and height of triangle ABC, we can calculate its area. The formula for the area of a triangle is:

Area = (1/2) * base * height

Plugging in the values, we have:

Area = (1/2) * 12 * 8
Area = 48

Therefore, the area of triangle ABC is 48 square meters, rounded to the nearest tenth.

since the bases are in the ratio of 2/3,

the areas are in the ratio of (2/3)^2 = 4/9

A(ABC) = (4/9)*(1/2)(18)(12) = 48