Question

find the surface area of a square pyramid with side length 1 m and slant height 4 m.

Explanation:

Step1: Calculate base - area

The base is a square with side length $a = 1$m. The area of the base $B=a^{2}=1^{2}=1$m².

Step2: Calculate area of one triangular face

The formula for the area of a triangle is $A_{\triangle}=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height. Here, the base of each triangular face is the side - length of the square base ($b = 1$m) and the height is the slant height ($h = 4$m). So, $A_{\triangle}=\frac{1}{2}\times1\times4 = 2$m².

Step3: Calculate total area of triangular faces

A square pyramid has 4 triangular faces. So the total area of the triangular faces $A_{triangles}=4\times A_{\triangle}=4\times2 = 8$m².

Step4: Calculate surface area

The surface area $SA$ of a square pyramid is the sum of the base area and the total area of the triangular faces. So, $SA=B + A_{triangles}=1+8=9$m².

Answer:

$9$m²