Question

Find the area of the base, lateral area, and total area.

Answer 1

First, we find the area of the base,

The base is a rectangle

`\text{Area of base = length }*\text{ width}`

Length = 24m, Width = 4m

Therefore,

`\begin{gathered} \text{Area of base = 24m }*\text{ 4m} \\ \text{Area of base = 96m}^2 \end{gathered}`

Finding, Lateral area

`\begin{gathered} \text{Lateral Area = sum of area of sides} \\ \text{Lateral Area = 2(lw) + 2(wh)} \end{gathered}`

Length = 24m, width = 4m, height = 2m

Therefore,

`\begin{gathered} \text{Lateral Area = 2(24m }*\text{ 4m) + 2(4m }*\text{ 2m)} \\ LateralArea=2(96m^2)+2(8m^2\text{)} \\ \text{Lateral Area = 192m}^2+16m^2 \\ \text{Lateral Area = 208m}^2 \end{gathered}`

Finding the total surface area,

The total surface area is given as

`\text{Total Surface Area =2lh + 2lw + 2wh}`

Therefore,

`\begin{gathered} \text{Total Surface area = 2(24m }*\text{ 2m) + 2(24m }*4m)\text{ + 2(4m }*2m) \\ \text{Total Surface Area = 2(48m}^2)\text{ + 2}(96m^2)+2(8m^2) \\ \text{Total Surface Area =96m}^2+192m^2+16m^2 \\ \text{Total Surface Area = 304m}^2 \end{gathered}`