type the correct answer in the box. use numerals instead of words. the composite figure shown has a surface…

Explanation:

Step1: Calculate surface - area components

1. Base of the prism: The base of the rectangular prism has an area (A_{base}=18\times10 = 180) square centimeters.
2. Two side - faces of the prism: Two side - faces of the prism have areas (A_{1}=18x) and (A_{2}=10x), and their combined area is (2(18x + 10x)=2\times(28x)=56x) square centimeters.
3. Four triangular faces of the pyramid:
   • The slant height of the triangular face with base 18 cm is 12 cm. The area of one such triangular face is (A_{triangle1}=\frac{1}{2}\times18\times12 = 108) square centimeters, and the area of two such faces is (2\times108 = 216) square centimeters.
   • The slant height of the triangular face with base 10 cm is 12 cm. The area of one such triangular face is (A_{triangle2}=\frac{1}{2}\times10\times12=60) square centimeters, and the area of two such faces is (2\times60 = 120) square centimeters.
4. Total surface - area formula: The total surface area (S) of the composite figure is (S = A_{base}+56x+216 + 120). We know that (S = 844) square centimeters. So, (180+56x+216 + 120=844).

Step2: Simplify the equation

Combine like - terms: (180+216+120+56x=844). (516+56x=844). Subtract 516 from both sides: (56x=844 - 516). (56x=328).

Step3: Solve for (x)

Divide both sides by 56: (x=\frac{328}{56}=\frac{41}{7}\approx5.86).

Answer:

(\frac{41}{7})