Answer: surface area = 142.2 feet²
Step-by-step explanation:
The right prism has 2 triangular faces whose base is 4 feet and the height is 3.5 feet. The formula for determining the area of each is expressed as
Area = 1/2 × base × height
Area of both faces = 2 × 1/2 × 4 × 3.5 = 14 ft²
Considering the rectangular sides, Area of the base is 4 × 10 = 40 ft²
Area of the end is 3.5 × 10 = 35 ft²
To determine the width of the rectangular top, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Width = hypotenuse
Opposite side = 3.5
Adjacent side = 4
Width² = 3.5² + 4² = 28.25
Width = √28.25 = 5.32 feet
Area of rectangular top = 5.32 × 10 = 53.2 feet
Therefore, the approximate surface area of this right prism is
14 + 40 + 35 + 53.2 = 142.2 feet²
