Find the surface area of the right prism with the given features.
The bases are right trapezoids with bases of lengths 8 and 14 perpendicular to one side of length 18; height = 11.
so, the area is two trapezoids and four rectangles
2[(8+14)/2 * 18] + 8*11 + 14*11 + 18*11 + 11√(6^2+18^2)
To find the surface area of the right prism, you need to calculate the areas of all its faces and then add them up.
First, let's find the area of the two bases. Since the bases are right trapezoids, you can use the formula for the area of a trapezoid, which is (1/2)(b1 + b2)(h), where b1 and b2 are the lengths of the bases and h is the height.
For the first base:
b1 = 8
b2 = 14
h = 11
The area of the first base is (1/2)(8 + 14)(11) = 99 units^2.
For the second base, the dimensions are the same, so the area is also 99 units^2.
Next, let's find the areas of the three rectangular faces. Since the prism is a rectangular prism, the areas of these faces are simply the length times the width.
The length of the rectangular faces is 18, and the height is 11. So, the areas of these three faces are:
1. Face 1: 18 * 11 = 198 units^2
2. Face 2: 18 * 11 = 198 units^2
3. Face 3: 18 * 8 = 144 units^2
Lastly, add up the areas of all the faces to find the surface area of the right prism:
Surface area = Area of the bases + Area of the rectangular faces
Surface area = (99 + 99) + (198 + 198 + 144)
Surface area = 732 units^2.
Therefore, the surface area of the right prism with the given features is 732 square units.