Question

What is the area of the base of a rectangular prism that has a 9mm width an 8mm height and a 14mm length?

Answer 1

The area of the base of rectangular prism is 126 mm².

Step-by-step explanation:

Given :

• 
  `\small\red\bull` Length of prism = 14mm
• 
  `\small\red\bull` Width of prism = 9mm
• 
  `\small\red\bull` Heights of prism = 8mm

To Find :

• 
  `\small\orange\bull` Volume of prism
• 
  `\small\orange\bull` Base area of prism

Using Formulas :

`\star\small{\underline{\boxed{\sf{\pink{Volume_((Prism)) = lwh}}}}}`

• 
  `\small\blue\star` l = length
• 
  `\small\blue\star` w = width
• 
  `\small\blue\star` h = height

`\star\small{\underline{\boxed{\sf{\pink{Volume_((Prism)) =bh}}}}}`

• 
  `\small\green\star` b = base area
• 
  `\small\green\star` h = height

Solution :

Finding the volume of prism by substituting the values in the formula to :

`\begin{gathered} \qquad\dashrightarrow{\sf{Volume_((Prism)) = lwh}} \\ \\ \qquad\dashrightarrow{\sf{Volume_((Prism)) = l * w * h}} \\ \\ \qquad\dashrightarrow{\sf{Volume_((Prism)) = 14 * 9 * 8 }} \\ \\ \qquad\dashrightarrow{\sf{Volume_((Prism)) = 14* 72}} \\ \\ \qquad\dashrightarrow{\sf{Volume_((Prism)) =1008 \: {mm}^(3)}} \\ \\ \qquad\star{\small{\underline{\boxed{\frak{\purple{Volume_((Prism)) = 1008 \: {mm}^(3)}}}}}}\end{gathered}`

Hence, the volume of prism is 1008 mm³.

`\rule{220}2`

Finding the base area of prism by substituting the values in the formula :

`\begin{gathered} \qquad{\dashrightarrow{\sf{Volume_((Prism)) =bh}}} \\ \\ \qquad{\dashrightarrow{\sf{Volume_((Prism)) =b * h}}} \\ \\ \qquad{\dashrightarrow{\sf{1008=b * 8}}} \\ \\ \qquad{\dashrightarrow{\sf{b = 1008 / 8}}} \\ \\ \qquad{\dashrightarrow{\sf{b = (1008)/(8)}}} \\ \\ \qquad{\dashrightarrow{\sf{b = \cancel{(1008)/(8)}}}} \\ \\ \qquad{\dashrightarrow{\sf{b = 126 \: {mm}^(2)}}} \\ \\ \qquad\star{\small{\underline{\boxed{\frak{\purple{Base \: Area = 126\: {mm}^(2)}}}}}}\end{gathered}`

Hence, the base area of prism is 126 mm².

`\rule{300}{1.5}`

Answer 2

The area of the base is 126 mm².

Explanation:

Given:

A rectangular prism that has a 9mm width and 8mm height and a 14mm length.

Now, to find the area of the base of the rectangular prism.

The dimensions of rectangular prism are:

Length = 14 mm.

Width = 9 mm.

Height = 8 mm.

Now, to get the volume of rectangular prism by putting formula:

`Volume=length* width* height\\\\Volume=14* 9* 8\\\\Volume=1008\ mm^3.`

Thus, the volume of rectangular prism is 1008 mm³.

Now, to get the area of the base we put formula:

`Volume=base\ area* height \\\\1008=base\ area* 8`

Dividing both sides by 8 we get:

`126=base\ area\\\\Base\ area = 126\ mm^2.`

Therefore, the area of the base is 126 mm².