Question

Can you please help me out with a question

Answer 1

A square pyramid has 5 faces. A base square and 4 triangles. The total surface area is a sum of the area of the individual faces.

`\begin{gathered} \text{Area of base square = l}^2\text{ where } \\ l=\text{ length of side = }16 \\ \text{Therefore area = 16}^2\text{ = 256 sq units} \end{gathered}`
`\begin{gathered} \text{Area of traingle = }(1)/(2)\text{ }* base\text{ }* perpendicular\text{ height} \\ \text{where base = }10 \\ \text{Perpendicular height will be obtained from pythagoras theorem } \\ Opp\text{= }\sqrt[]{hyp^2-\text{adj}} \\ \text{= }\sqrt[]{10^2-8^2}=6 \\ \end{gathered}`

We now have to find the area of the other 4 faces and sum it all

`\text{Area of the 4 triangles =4( }(1)/(2)*16\text{ }*\text{ 6) = 192 sq units }`

Total surface area of the pyramid = area of base square + area of 4 triangles

`=\text{ 192 +256 = 448 sq units}`