Question

las bases de un prisma recto son dos triangulos rectangulos cuyos catetos miden 1.5 cm y 1.8 cm, respectivamente, el prisma tiene una altura de 4.5cm. calcula su area total y volumen

Answer 1

Part 1) The surface area is
`SA=35.1\ cm^(2)`

Part 2) The volume is equal to
`V=12.15\ cm^(3)`

Explanation:

The question in English is

The bases of a right prism are two rectangle triangles whose legs measure 1.5 cm and 1.8 cm, respectively, the prism has a height of 4.5 cm. calculates its total surface area and volume

Part 1) Find the surface area

The surface area is equal to

`SA=2B+Ph`

where

B is the area of the base

P is the perimeter of the base

h is the height of the prism

Find the area of the base B

`B=(1.5)(1.8)=2.7\ cm^(2)`

Find the perimeter of the base P

`P=2*(1.5+1.8)=6.6\ cm`

we have

`h=4.5\ cm`

substitute the values

`SA=2(2.7)+(6.6)(4.5)=35.1\ cm^(2)`

Part 2) Find the volume

The volume is equal to

`V=Bh`

where

B is the area of the base

h is the height of the prism

we have

`B=2.7\ cm^(2)\\ h=4.5\ cm`

substitute

`V=(2.7)(4.5)=12.15\ cm^(3)`