The square pyramid shown below has a slant height of 171717 units and a vertical height of 151515 units. What is the length of one of the pyrmaids base?
Mathematics · High School · Thu Feb 04 2021
Answered on
We have the slant length and vertical length of a square pyramid, and have to find the length of the base.
We all know how a square pyramid look like,
It make a right angle triangle with the vertical length, slant length and half of the base
And we know the Pythagoras theorem too,
So let's calculate the half of the base with it,
Let assume:
Slant length= s= 171717 units
vertical length= v= 151515 units
half of the base= a= ?
(s)²= (v)²+(a)²
(171717)²= (151515)² + a²
29486728089 = 22956795225 + a²
a² = 29486728089 - 22956795225
a² = 6529932864
a = √6529932864
a = 80808
∴ half of the base is 80808
So base= 2x80808
Base of the square pyramid= 161616 units.