Questions: Choose the best answer. Find the total surface area for a rectangular prism with a length of 82 cm, a width of 75 cm, and a height of 21 cm. Let the faces with the dimensions of the length and width be the prism bases. Calculate the total surface area: SA. 21,050 cm^2 129,150 cm^2 18,894 cm^2

Solution Steps

To find the total surface area of a rectangular prism, we need to calculate the area of all six faces and sum them up. The formula for the surface area \( SA \) of a rectangular prism is given by: \[ SA = 2lw + 2lh + 2wh \] where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

Given:

• Length \( l = 82 \) cm
• Width \( w = 75 \) cm
• Height \( h = 21 \) cm

We will use these values in the formula to calculate the total surface area.

To find the total surface area \( SA \) of the rectangular prism, we use the formula: \[ SA = 2lw + 2lh + 2wh \] Substituting the given dimensions \( l = 82 \, \text{cm} \), \( w = 75 \, \text{cm} \), and \( h = 21 \, \text{cm} \): \[ SA = 2(82 \times 75) + 2(82 \times 21) + 2(75 \times 21) \]

Calculating each term:

• \( 82 \times 75 = 6150 \)
• \( 82 \times 21 = 1722 \)
• \( 75 \times 21 = 1575 \)

Now substituting back into the surface area formula: \[ SA = 2(6150) + 2(1722) + 2(1575) = 12300 + 3444 + 3150 = 18894 \, \text{cm}^2 \]

Final Answer