Question

Find the lateral area for the prism. L.A. =
Find the total area for the prism. T.A. =

Answer 1

The lateral area of the prism is given by:
LA=[area of the two triangles]+[area of the lateral rectangles]
hypotenuse of the triangle will be given by Pythagorean:
c^2=a^2+b^2
c^2=6^2+4^2
c^2=52
c=sqrt52
c=7.211'
thus the lateral area will be:
L.A=2[1/2*4*6]+[6*8]+[8*7.211]
L.A=24+48+57.69
L.A=129.69 in^2

The total are will be given by:
T.A=L.A+base area
base area=length*width
=4*8
=32 in^2
thus;
T.A=32+129.69
T.A=161.69 in^2

Answer 2

Part 1)
`LA=(80+16√(13))\ in^(2)`

Part 2)
`TA=(104+16√(13))\ in^(2)`

Explanation:

Part 1) Find the lateral area of the prism

we know that

The lateral area of the prism is equal to

`LA=Ph`

where

P is the perimeter of the base

h is the height of the prism

Applying the Pythagoras Theorem

Find the hypotenuse of the triangle

`c^(2)=4^(2)+6^(2)\\ \\c^(2)=52\\ \\c=2√(13)\ in`

Find the perimeter of triangle

`P=4+6+2√(13)=(10+2√(13))\ in`

Find the lateral area

`LA=Ph`

we have

`P=(10+2√(13))\ in`

`h=8\ in`

substitutes

`LA=(10+2√(13))*8=(80+16√(13))\ in^(2)`

Part 2) Find the total area of the prism

we know that

The total area of the prism is equal to

`TA=LA+2B`

where

LA is the lateral area of the prism

B is the area of the base of the prism

Find the area of the base B

The area of the base is equal to the area of the triangle

`B=(1)/(2)bh`

substitute

`B=(1)/(2)(6)(4)=12\ in^(2)`

Find the total area of the prism

`TA=LA+2B`

we have

`B=12\ in^(2)`

`LA=(80+16√(13))\ in^(2)`

substitute

`TA=(80+16√(13))+2(12)=(104+16√(13))\ in^(2)`