Question

A written explanation solving the question how much fluid is needed using the Pythagorean method and finding the area of the triangle

Answer 1

793 liters of washing fluid is needed

Explanation:

step 1

Find the slant height of the triangular faces of pyramid

we know that

The lateral area of a square pyramid is equal to the area of its four triangular faces

so

`LA=4[(1)/(2)bl]`

where

b is the base of triangle (is the same that the length of the square base)

l is the slant height

To find out the slant height we need to apply the Pythagorean Theorem

so

`l^2=(b/2)^2+h^2`

we have

`b=35.42\ m`

`h=21.64\ m`

substitute

`l^2=(35.42/2)^2+21.64^2`

`l^2=781.9337`

`l=27.96\ m`

step 2

Find the lateral area of the pyramid

`LA=4[(1)/(2)bl]`

we have

`l=27.96\ m`

`b=35.42\ m`

substitute

`LA=4[(1)/(2)(35.42)(27.96)]`

`LA=1,980.6864\ m^2`

step 3

Find out how much window washing fluid is needed

we know that

2 L of washing fluid cover 5 square meters

so

using proportion

`(2)/(5)\ (L)/(m^2)=(x)/(1,980.6864)\ (L)/(m^2)\\\\x=1,980.6864(2)/5\\\\x= 792.27\ L`

Round up

793 liters of washing fluid is needed