1. **Problem statement:** We have a large right triangle composed of smaller geometric figures with given areas: two small right triangles each with area 4.5, and three rectangles with areas 10, 5, and 6. 2. **Goal:** Calculate the total area of the large right triangle by summing the areas of all smaller parts. 3. **Given areas:** - Small triangle 1: $A_1 = 4.5$ - Small triangle 2: $A_2 = 4.5$ - Rectangle 1: $A_3 = 10$ - Rectangle 2: $A_4 = 5$ - Rectangle 3: $A_5 = 6$ 4. **Formula:** The total area $A$ of the large triangle is the sum of all smaller areas: $$ A = A_1 + A_2 + A_3 + A_4 + A_5 $$ 5. **Calculation:** $$ A = 4.5 + 4.5 + 10 + 5 + 6 = 30 $$ 6. **Answer:** The area of the entire large right triangle is **30**.