Q1. - Geometry

Question

Refer to rectangular solids with dimensions l, w and h. Complete the following table.

$\begin{array}{cc}l& 6\\ w& 4\\ h& 2\\ \text{L.A.}& \\ \text{T.A.}& \\ V& \end{array}$

Step-by-Step Solution

Answer

$\begin{array}{cc}l& 6\\ w& 4\\ h& 2\\ \text{L.A.}& 40\\ \text{T.A.}& 88\\ V& 48\end{array}$

Step 1. Given information.

The length, width and height of a rectangle are 6, 4 and 2 respectively.

Step 2. Write the concept.

The lateral area of the rectangle is given by:

$\text{L.A.}=\text{Perimeter}\times \text{Height}$

 

The total area of the rectangle is given by:

$\text{T.A.}=\text{L.A.+}2\left(\text{Base}\right)$

 

The volume of rectangle is given by:

$\text{V}=l\times w\times h$

Step 3. Determine the value.

Now, substitute all the given values in the formula.

$\begin{array}{c}\text{L.A.}=2(l+w)\times h\\ =2(6+4)\times 2\\ =2\left(10\right)\times 2\\ =20\times 2\\ =40{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

And

$\begin{array}{c}\text{T.A.}=\text{40+}2(\text{6}\times \text{4})\\ =\text{40+}2\left(24\right)\\ =\text{40+}48\\ =88{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

And the volume is

$\begin{array}{c}\text{V}=6\times 4\times 2\\ =24\times 2\\ =48{\text{\hspace{0.17em}\hspace{0.17em}unit}}^3\end{array}$