jillian wants to find the surface area of a pyramid the base is a square with sides that are 4 inches long the other faces are isosceles triangles the ratio of the height of each triangle to its base is 3:1 part a: give the Base length and the height of each triangular face part b : find the combined area of the Triangular faces part c: find the surface area of the pyramid

check the picture below.

so the pyramid is more or less like so, keep in mind that the base of it is a square, thus is called a "square" pyramid.

a)

since the height : base are on a 3:1 ratio, namely the height is three times as large as the base, if the base of a triangular face is 4, then the height is 3(4), as you see there.



b)

there are 4 triangles, recall that A = 1/2 bh, thus

[tex]\bf \stackrel{\textit{area of the four triangles}}{4\left[ \cfrac{1}{2}(4)(12) \right]}[/tex]



c)

well, you already know the lateral area, namely the area of the four triangles, the total surface area is just that plus the area of the base, well, the base is just a 4x4 square, so add that to the triangle's area, and that's the total surface area.