Find the lateral surface area and the total surface area.

Lateral surface area =176 square units.

Total surface area=226 square units

Step-by-step explanation:

This is a trapezoidal prism. A prism is named based on it's parallel bases and a prism other sides are some kind of parallelogram.

Lateral surface area doesn't include the bases in the area calculation.

So we won't find the area of the trapezoids.

So for the lateral area of this trapezoidal prism I will need to 4 areas and add them. The areas needed are that of rectangles. The formula for the area of a rectangle is height times base.

There are two rectangles with dimensions 8 units by 6 units. The area of a 8 by 6 rectangle is 48 units square (I did 8 times 6).

So far our lateral area is 48+48+(something else goes here).

We have one rectangle with dimensions 8 units by 3 units. The area of a 8 by 3 rectangle is 24 units square (I did 8 times 3).

So now we have 48+48+24+(one more number).

The last rectangle is in the back of the image.  It is a 8 unit by 7 unit rectangle. The area of a 8 by 7 rectangle is 56 square units. (I did 8 times 7).

Now finally we have our full sum for the lateral surface area which is 48+48+24+56=176 square units.

We need to now find the total surface area. This is the lateral area + remaining area. I'm saying we need to find the area of the two trapezoids.

The area of trapezoid is the average of the bases times the height.

So the top trapezoid has bases 7 units and 3 units. The height of the trapezoid is 5.

Average of bases of trapezoid =(7+3)/2=10/2=5

So the area of the top trapezoid is 5(5)=25 units squared.

Both trapezoids are the same so the total surface area is the lateral area+25+25 which equals 176+25+25=176+50=226 square units.

This prism is made up of 4 rectangles and 2 trapezoids.

Find the surface area:

Hence, the total surface area is 226 units.

The bases are the trapezoids on the top and bottom og the prism. So, just subtract.

226 - 50 = 176 units is the lateral surface area.

Best of Luck!