Question

Find the surface area of a square pyramid with side length 4 cm and slant height 3 cm.

Answer 1

40 cm²

Explanation:

The surface area of a square-based pyramid is made up of:

• A square base.
• 4 congruent triangular sides.

The area of a square is the square of its side length.

Given the side length of the square base is 4 cm, the area of the base is:

`\begin{aligned}\implies \sf Area\;of\;square\;base&=4^2\\&=4 \cdot 4\\&=16\;\sf cm^2\end{aligned}`

The area of a triangle is half the product of its base and height.

Given the base of the triangular side is 4 cm and its height is 3 cm, the area of one triangular side is:

`\begin{aligned}\implies \sf Area\;of\;one\;triangular\;side&=(1)/(2)\cdot 4 \cdot 3\\&=2 \cdot 3\\&=6\;\sf cm^2\end{aligned}`

Therefore, the total surface area of the square pyramid is:

`\begin{aligned}\implies \sf Total\;surface\;area&=\sf square\;base+ 4\; triangular\;sides\\&=\sf 16\;cm^2+4 \cdot 6\; cm^2\\&=\sf 16\; cm^2+24\;cm^2\\&=\sf 40\;\sf cm^2\end{aligned}`