Q82. - Algebra 2

Question

GEOMETRY

82. 82. The formula for the surface area SA of a rectangular prism is $SA=2lw+2lh+2wh$, where l represents length, w represents width, and h represents height. Find the surface area of the rectangular prism.

Step-by-Step Solution

Answer

Surface area of rectangular prism is 358 square inches 

Step 1 - Order for simplification

To evaluate any expression involving more than one operation, follow the below order of operations:

• First evaluate expressions inside grouping symbols like parentheses ( ) or brackets [ ].
• Evaluate the exponents.
• Perform Multiplication and division from left to right.
• Perform addition and subtraction from left to right.

Step 2 - Observation from image

From image, length of rectangular prism is 12 in. Its breadth is 5 in. and height is 7 in.

Substitute 12 for l, 5 for b, and 7 for h in given equation of surface area.

$SA=2\left(12\times 5\right)+2\left(12\times 7\right)+2\left(5\times 7\right)$

Step 3 - Simplify expression inside grouping symbol

To evaluate the value of the given expression, first use distributive property $ab+ac=a\left(b+c\right)$, then simplify the expression inside the parenthesis as shown below

$\begin{array}{c}SA=2\left(12\times 5\right)+2\left(12\times 7\right)+2\left(5\times 7\right)\\ =2\left[\left(12\times 5\right)+\left(12\times 7\right)+\left(5\times 7\right)\right]\\ =2\left[60+84+35\right]\\ =2\left(179\right)\end{array}$

Step 4 - Multiply 2 with 179

Now, to simplify further multiply the numbers to get 

$\begin{array}{c}SA=2\times 179\\ =358\end{array}$