Given:
A square base pyramid with base length 6 cm and the slant height is 4 cm.
To find:
The lateral surface area of the given square pyramid.
Solution:
The lateral surface area of the given square pyramid is equal to the areas of 4 congruent triangles with base 6 cm and height 4 cm.
Area of a triangle is:
[tex]Area=\dfrac{1}{2}\times base\times height[/tex]
So, the area of one triangle or one side of the given pyramid is:
[tex]A_1=\dfrac{1}{2}\times 6\times 4[/tex]
[tex]A_1=\dfrac{24}{2}[/tex]
[tex]A_1=12[/tex]
Now, the lateral surface area of the given square pyramid is 4 times the area of one triangle.
[tex]LA=4A_1[/tex]
[tex]LA=4(12)[/tex]
[tex]LA=48[/tex]
Therefore, the lateral surface area of the given square pyramid is 48 cm².