Answer:
4.8 units^2
Step-by-step explanation:
Hello! To find the area of this triangle, we need to know both the base and the height. Neither is specifically given.
We can find the height (CD) as follows:
3^2 - 1.8^2 = 5.76, so CD has the length sqrt(5.76) = 2.4.
Triangles ACD and ABC are similar. Therefore, the following equatin of ratios holds:
1.8 CD 2.4
----- = ------- = --------
3.0 AB AB
Then 1.8AB = 3.0(2.4), or AB = 7.2/1.8 = 4.
So the height of triangle ABC is 2.4 units and the length of the base is 4 units.
Therefore, the area of this triangle is A = (1/2)(base)(height), or
A = (1/2)(4 units)(2.4 units) = 4.8 units^2
