Question

surface area of a pyramid. The base is a square with sides 4 inches long. the other faces are isosceles triangles. the ratio of the height of each triangle to its base is 3:2. Give the base length and the height of each triangular face

Answer 1

Base of each triangular face = 4 inches

Height of each triangular face = 6 inches

Explanation:

The length of each side of the square base is the base of each isosceles triangle forming the pyramid.

We know from our problem that the ratio of the height of each triangle to its base is 3:2, so
`(height)/(base) =(3)/(2)`. We also know that the base is a square with sides 4 inches long, since the bade of the square is the base of the isosceles triangle,
`base=4`.

Replacing the value of the base in our proportion:

`(height)/(base) =(3)/(2)`

`(height)/(4) =(3)/(2)`

Multiply both sides by 4

`(height)/(4)*4 =(3)/(2)*4`

`height=(3*4)/(2)`

`height=(12)/(2)`

`height=6`

We can conclude that he base of each isosceles triangle is 4 inches and its height is 6 inches.