Question

The lateral edge of a square prism is 30 cm long and it is inclined at an

angle of 70 degrees with the base. If the volume of the prism is 1,500 cm3,
1. what is the base edge?
2. What is the lateral area of the prism?
3. What is the total area of the square prism?

Answer 1

1

`B  =  7.07 \  cm`

2

`A  =848.4 cm^2`

3

`A_T  = 948.37 \  cm^2`

Explanation:

From the question we are told that

The lateral edge of a square prism is
`d = 30 \ cm = 0.3 \ m`

The angle of inclination is
`\theta = 70^o`

The volume of the prism is
`V = 1500\ cm^3`

Generally the base of the prism is mathematically represented as

`B  =  \sqrt{(V)/( d) }`

=>
`B  =  \sqrt{(1500)/( 30) }`

=>
`B  =  7.07 \  cm`

Generally the lateral area of the prism is mathematically represented as

`A  = 4 *  B  *  d`

=>
`A  = 4 *  7.07  *  30`

=>
`A  =848.4 cm^2`

Generally the total area of the prism is mathematically represented as

`A_T  =  2 * B  + A`

=>
`A_T  =  2 * (7.07)  + 848.4`

=>
`A_T  = 948.37 \  cm^2`