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A rectangular prism has a base length of 6 units, base width of 5 units, and height of 4 units. The bases are shaded.
The lateral area is
The area of the two bases together is
The total surface area is
Answer:
The lateral area is 88 units²
The area of the two bases together is 60 units²
The total surface area is 148 units²
Step-by-step explanation:
The lateral area of a rectangular prism is the sum of the areas of the side faces
The formula of the lateral area of a rectangular prism is LA = perimeter of its base (p) × its height (h)
The formula of the total surface area of it is SA = LA + area of its two bases
∵ The rectangular prism has a base length of 6 units, base
width of 5 units, and height of 4 units
∴ l = 6 units
∴ w = 5 units
∴ h = 4 units
∵ The dimensions of the base area the length and the width
∵ The perimeter of a rectangle = 2(l + w)
∴ The perimeter of the base = 2(6 + 5) = 2(11)
∴ The perimeter of the base = 22 units
Use the formula of the lateral area to find it
∵ LA = p × h
∴ LA = 22 × 4 = 88 units²
The lateral area is 88 units²
∵ The area of a rectangle = l × w
∴ The area of one base of the rectangular prism = 6 × 5
∴ The area of one base = 30 units²
- Multiply it by 2 to find the area of the two bases
∴ The area of two bases = 30 × 2 = 60 units²
The area of the two bases together is 60 units²
Use the formula of the total surface area to find it
∵ SA = LA + area of the two bases
∴ SA = 88 + 60 = 148 units²
The total surface area is 148 units²
