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

Answer:

The total volume of the prism is 32.49 cubic centimeters.

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

Step-by-step 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

$V_{prism}=\frac{1}{2} B \times h$

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

$B=\frac{\sqrt{3} }{4} l^{2}$

Where $l= 5 \ cm$

$B=\frac{\sqrt{3} }{4} l^{2}=\frac{\sqrt{3} }{4}(5 \ cm)^{2} \approx 10.83 \ cm^{2}$

Replacing the base area in the volume formula, we have

$V_{prism}=\frac{1}{2} B \times h=\frac{1}{2} (10.83 \ cm^{2} )(6 \ cm)\\V_{prism}=32.49 \ cm^{3}$

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.

$S_{total}= 3(5 \times 6) + 2(10.83)=90+21.66 = 111.66 \ cm^{2}$

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