Question

Halla el área total y el volumen de un prisma triangular de altura 6cm y base un triángulos equilátero de lado 5cm. Redondea el resultado a dos cifras decimales

Answer 1

The total volume of the prism is 32.49 cubic centimeters.

The total surface area of the figure is 111.66 square centimeters.

Explanation:

This problem is about finding the volume of a prism which base is an equilateral triangle.

The volume of the prism would be defined as

`V_(prism)=(1)/(2) B * h`

Where
`B` is the area of the base and
`h` is the height of the prism.

The area of the equilateral triangle at the base is

`B=(√(3) )/(4) l^(2)`

Where
`l= 5 \ cm`

`B=(√(3) )/(4) l^(2)=(√(3) )/(4)(5 \ cm)^(2) \approx 10.83 \ cm^(2)`

Replacing the base area in the volume formula, we have

`V_(prism)=(1)/(2) B * h=(1)/(2) (10.83 \ cm^(2) )(6 \ cm)\\V_(prism)=32.49 \ cm^(3)`

Therefore, the total volume of the prism is 32.49 cubic centimeters.

Now, the total surface area would be the sum of three rectangle faces and two triangles faces.

`S_(total)= 3(5 * 6) + 2(10.83)=90+21.66 = 111.66 \ cm^(2)`

Therefore, the total surface area of the figure is 111.66 square centimeters.