Question

Find the Lateral Area and Surface Area of the figure.1310Perimeter of the base =Slant height =(Note: 13 is NOT the slant height)Area of the base =square unitsL.A. =square unitsS.A. =square unitsBlank 1:Blank 2:Blank 3:Blank 4:Blank 5:

Answer 1

The formula for the perimeter of the base (square) is ,

`P=4a`

where,

`a=\text{side of the base}=10`

Therefore,

`\text{Perimeter}=4*10=40\text{units}`

Let us now solve for the slant height(l),

To solve for l, we will make use of Pythagoras theorem

`\begin{gathered} 13^2=l^2+5^2 \\ 169=l^2+25 \\ 169-25=l^2 \\ 144=l^2 \\ \Rightarrow l^2=144 \\ l=\sqrt[]{144}=12\text{units} \\ l=12\text{units} \end{gathered}`

Hence, the slant height is 12units.

The formula for the Lateral Area(LA) is given as,

`LA=Pl`

Therefore,

`\begin{gathered} LA=40\text{units}*12units=480units^2 \\ LA=480unit^2^{} \end{gathered}`

Hence, the Lateral area is 480unit².

The formula for the Surface area(SA) is,

`\begin{gathered} SA=\text{base area+lateral area} \\ \end{gathered}`

where the base area(B) is,

`\begin{gathered} B=a^2 \\ a=10units \\ B=(10\text{unit)}^2 \\ B=100\text{units}^2 \end{gathered}`

Hence, the Surface area is,

`\begin{gathered} SA=100\text{units}^2+480\text{units}^2 \\ SA=580\text{units}^2 \end{gathered}`

Hence, the Surface area is 580unit².