Respuesta :
Answer:
The area of the base is 126 mm².
Step-by-step 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:
[tex]Volume=length\times width\times height\\\\Volume=14\times 9\times 8\\\\Volume=1008\ mm^3.[/tex]
Thus, the volume of rectangular prism is 1008 mm³.
Now, to get the area of the base we put formula:
[tex]Volume=base\ area\times height \\\\1008=base\ area\times 8[/tex]
Dividing both sides by 8 we get:
[tex]126=base\ area\\\\Base\ area = 126\ mm^2.[/tex]
Therefore, the area of the base is 126 mm².
Answer:
The area of the base of rectangular prism is 126 mm².
Step-by-step explanation:
Given :
- [tex]\small\red\bull[/tex] Length of prism = 14mm
- [tex]\small\red\bull[/tex] Width of prism = 9mm
- [tex]\small\red\bull[/tex] Heights of prism = 8mm
To Find :
- [tex]\small\orange\bull[/tex] Volume of prism
- [tex]\small\orange\bull[/tex] Base area of prism
Using Formulas :
[tex]\star\small{\underline{\boxed{\sf{\pink{Volume_{(Prism)} = lwh}}}}}[/tex]
- [tex]\small\blue\star[/tex] l = length
- [tex]\small\blue\star[/tex] w = width
- [tex]\small\blue\star[/tex] h = height
[tex]\star\small{\underline{\boxed{\sf{\pink{Volume_{(Prism)} =bh}}}}}[/tex]
- [tex]\small\green\star[/tex] b = base area
- [tex]\small\green\star[/tex] h = height
Solution :
Finding the volume of prism by substituting the values in the formula to :
[tex]\begin{gathered} \qquad\dashrightarrow{\sf{Volume_{(Prism)} = lwh}} \\ \\ \qquad\dashrightarrow{\sf{Volume_{(Prism)} = l \times w \times h}} \\ \\ \qquad\dashrightarrow{\sf{Volume_{(Prism)} = 14 \times 9 \times 8 }} \\ \\ \qquad\dashrightarrow{\sf{Volume_{(Prism)} = 14\times 72}} \\ \\ \qquad\dashrightarrow{\sf{Volume_{(Prism)} =1008 \: {mm}^{3}}} \\ \\ \qquad\star{\small{\underline{\boxed{\frak{\purple{Volume_{(Prism)} = 1008 \: {mm}^{3}}}}}}}\end{gathered}[/tex]
Hence, the volume of prism is 1008 mm³.
[tex]\rule{220}2[/tex]
Finding the base area of prism by substituting the values in the formula :
[tex] \begin{gathered} \qquad{\dashrightarrow{\sf{Volume_{(Prism)} =bh}}} \\ \\ \qquad{\dashrightarrow{\sf{Volume_{(Prism)} =b \times h}}} \\ \\ \qquad{\dashrightarrow{\sf{1008=b \times 8}}} \\ \\ \qquad{\dashrightarrow{\sf{b = 1008 \div 8}}} \\ \\ \qquad{\dashrightarrow{\sf{b = \dfrac{1008}{8}}}} \\ \\ \qquad{\dashrightarrow{\sf{b = \cancel{\dfrac{1008}{8}}}}} \\ \\ \qquad{\dashrightarrow{\sf{b = 126 \: {mm}^{2}}}} \\ \\ \qquad\star{\small{\underline{\boxed{\frak{\purple{Base \: Area = 126\: {mm}^{2}}}}}}}\end{gathered}[/tex]
Hence, the base area of prism is 126 mm².
[tex]\rule{300}{1.5}[/tex]
