The bases of a prism are right triangles with side lengths 6 meters,
sters, and 10 meters. the height of the prism is 3 meters. what is
who lateral area of the prism? what is the total surface area?

Part a) The lateral area of the prism is

Part b) The surface area of the prism is

Step-by-step explanation:

Part a) What is  the lateral area of the prism?

we know that

The lateral area of the prism is

where

P is the perimeter of the base

H is the height of the prism

we have

The perimeter of the base is

Find the hypotenuse of the right triangle

Applying the Pythagoras Theorem

Find the perimeter of the base P

Find the lateral area of the prism

Part b) What is the total surface area?

The total surface area is

where

LA is the lateral area

B is the area of the base

Find the area of the base

Remember that the base is a triangle so

we have

substitute

Find the surface area of the prism

we have

substitute

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225