Question

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

Answer 1

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

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



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.

Answer 2

Answer:

a.Length of base=4 inches

Length of height=12 inches

b.Area of  triangular faces=96 square inches

c.Surface area of pyramid=112 square inches

Step-by-step explanation:

We are given that base of pyramid is square shaped with side 4 inches long

Other faces are isosceles triangles

We are given that ratio of height of each triangle  to its base =3:1

a.We have to find the length of base and the height of each triangular face

Length of base=4 inches

Height is 3 times the base

Therefore, length of height=$3\times 4=12 inches$

b.There are 4 triangular faces

We know that area of triangle=$\frac{1}{2}\times b\times h$

Using this formula

Area of one triangular face =$\frac{1}{2}\times 12\times 4$=24 square inches

Area of 4 triangular faces=$4\times 24=96 square inches$

c. Surface area of pyramid=area of 4 triangular faces+area of square

Surface area of pyramid =$96+4\times 4=96+16=112 square inches$