Question

hanh and her brother are painting a sandbox shaped like a rectangular prism. they want to paint only the outsides of the four rectangular sides. how many square feet will be painted? (not drawn to scale) 1 ft 5 ft 6 ft a 24 ft² b 22 ft² c 20 ft² d 41 ft²

Explanation:

Step1: Identify side - area formulas

The four sides of the rectangular prism are two pairs of rectangles. The areas of rectangles are calculated by $A = lw$ (length times width).

Step2: Calculate areas of two types of sides

One pair of sides has dimensions $6$ ft (length) and $1$ ft (height), and the other pair has dimensions $5$ ft (length) and $1$ ft (height).
The area of the first - type side: $A_1=6\times1 = 6\ ft^{2}$, and since there are two such sides, their combined area is $2\times6 = 12\ ft^{2}$.
The area of the second - type side: $A_2 = 5\times1=5\ ft^{2}$, and their combined area is $2\times5 = 10\ ft^{2}$.

Step3: Calculate total painted area

The total area to be painted is $A=12 + 12=24\ ft^{2}$.

Answer:

A. $24\ ft^{2}$