Question

use formulas to find the lateral area and surface area of the prism. the lateral area of the prism is __ in squared. round to the nearest whole number as needed

Answer 1

• The lateral area of the prism is 900in².

,

• The total area of the prism is 954in².

Step-by-step explanation

The lateral area of a right triangle prism (AL) is given by:

`A_L=A_(r1)+A_(r2)+A_(r3)`

where Ar₁ represents the area of the first rectangle, Ar₂ the second, and Ar₃ the third. The area of a rectangle is given by:

`A_r=b* h`

We have that b₁ = 12in, b₂ = 15in, and we don't know the value for b₃. However, we can calculate it with the Pythagorean Theorem:

`b_2^2=b_1^2+b_3^2`
`b_3^=√(b_2^2-b_1^2)`
`b_3=√(15^2-12^2)=√(81)=9`

Then, the lateral area is the sum of Ar₁ , Ar₂, and Ar₃:

`A_(r1)=12*25=300`
`A_(r2)=15*25=375`
`A_(r3)=9*25=225`

Thus, the lateral area is:

`A_L=300+375+225=900in^2`

Finally, the total area (AT) is the addition of the area of the two bases (Ab) of the prism with the lateral area:

`A_b=(1)/(2)*9*12=54in^2`
`A_T=54+900=954in^2`