A rectangular prism has a base length of 6 units, base
width of 5 units, and height of 4 units. The bases are
shaded.

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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

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

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign