Question

Use the pyramid to the right. Find (a) the slant height, (b) the lateral area of the pyramid, (c) the surface area of the pyramid, and (d) the volume of the pyramid.

Answer 1

The slant height, l, is given as:

`\begin{gathered} l=\sqrt[]{8^2+6^2} \\ l=\sqrt[]{64+36} \\ l=\sqrt[]{100} \\ l=10\text{ in} \end{gathered}`

The lateral area is given by the formula:

`\begin{gathered} \text{Lateral Area= slant height }*\frac{perimeter\text{ of base}}{2} \\ \text{Lateral Area= 10}*(6+6+6+6)/(2) \\ \text{Lateral Area=10}*(24)/(2) \\ \text{Lateral Area=}(240)/(2) \\ \text{Lateral Area = 120 in}^2 \end{gathered}`

The surface area of the pyramid is given by:

`\begin{gathered} S\mathrm{}A_(pyramid)=\text{Area of the base + Lateral area} \\ S\mathrm{}A=\text{ (6}*6)+120_{} \\ S.A=36+120 \\ S\mathrm{}A=156in^2 \end{gathered}`

The volume of the pyramid is given by:

`\begin{gathered} V=(1)/(3)* base\text{ area}* height \\ V=(1)/(3)*(6*6)*8 \\ V=(1)/(3)*36*8 \\ V=96in^3 \end{gathered}`