Question

find the surface area and volume of the solid. round each measure to the nearest tenth, if necessary.

Explanation:

Step1: Calculate base - area of the triangular prism

The base is a triangle with base $b = 2.0$ cm and height $h = 2.4$ cm. The area of a triangle $A_{base}=\frac{1}{2}\times b\times h$.
$A_{base}=\frac{1}{2}\times2.0\times2.4 = 2.4$ $cm^{2}$

Step2: Calculate volume of the triangular prism

The volume of a prism $V=A_{base}\times l$, where $l = 4.0$ cm.
$V = 2.4\times4.0=9.6$ $cm^{3}$

Step3: Calculate areas of the rectangular faces

There are three rectangular faces.
Face 1: with dimensions $2.0$ cm and $4.0$ cm, area $A_{1}=2.0\times4.0 = 8.0$ $cm^{2}$
Face 2: with dimensions $2.4$ cm and $4.0$ cm, area $A_{2}=2.4\times4.0 = 9.6$ $cm^{2}$
Face 3: First, find the hypotenuse of the base - triangle using the Pythagorean theorem $c=\sqrt{2.0^{2}+2.4^{2}}=\sqrt{4 + 5.76}=\sqrt{9.76}\approx3.12$ cm. Then the area of the third rectangular face $A_{3}=3.12\times4.0\approx12.5$ $cm^{2}$

Step4: Calculate total surface area

The total surface area $A = 2A_{base}+A_{1}+A_{2}+A_{3}$
$A=2\times2.4 + 8.0+9.6+12.5=4.8+8.0+9.6+12.5 = 34.9$ $cm^{2}$

Answer:

Volume: $9.6$ $cm^{3}$
Surface - area: $34.9$ $cm^{2}$