Question in image

Question

Answer 1

First the question states to name the prism.

The name of this prism is called a triangular prism.

_____________

To find Lateral area of a triangular prism you need to apply this formula:

(a+b+c)*h

a=8

b=4

c=12

h=8

(8+4+12)*8

You plug in the values inside the equation and solve for LA.

(24)(8)=192

LA=192

The solution for LA is 192

ANS: 192

To find total area of a triangular prism you need to apply this formula:

A_tot=A_top+A_bot+A_lat

Since the lateral area is found plug in the value for A_lat

A_tot=A_top+A_bot+192

Now you need to find A_top and A_bot

A_top=1

__ sqrt((a+b+c)(b+c-a)(c+a-b)(a+b-c)

4

You plug in the values inside the equation to find the solution

a=8

b=4

c=12

A_top=1

__ sqrt(8+4+12)(4+12-8)(12+8-8)(8+4-12)=0

4

sqrt(0)=0

A_top=0

To find the bottom you need to apply this formula

A_bot=1

__ sqrt(a+b+c)(b+c-a)(c+a-b)(a+b-c)

4

a=8

b=4

c=12

Plug in the values in the equation to find A_bot

A_bot=1

__ sqrt(8+4+12)(4+12-8)(12+8-4)(8+4-12)

4

The solution should turn out to be 0

A_bot=0

Now you plug in the values to the total surface area formula

A_tot=A_top+A_bot+A_lat

A_top=0

A_bot=0

A_lat=192

Plug in the values in the equation

A_tot=0+0+192

A_tot=192

The solution to the total area is 192.

ANS: TA=192

Answer 2

Use Pythagoras to determine height of triangular face.

Use formula for area of triangle. Multiply by 2

Determine area of two rectangular faces

Add them all up.