# Thread: trying to calculate the surface area and volume of a prism

1. ## trying to calculate the surface area and volume of a prism

I believe i have solved the trapezoid sides of the prism. I just need to solve for the rectangular portion. I appreciate any help

A1= (a+b)h/2
+(5.6+4.5)7.2/2
=10.1(7.2)/2
a1=36.36*2sides
a1=72.7square meters

2. ## Re: trying to calculate the surface area and volume of a prism

Originally Posted by hotboxdriver
I believe i have solved the trapezoid sides of the prism. I just need to solve for the rectangular portion. I appreciate any help

A1= (a+b)h/2
+(5.6+4.5)7.2/2
=10.1(7.2)/2
a1=36.36*2sides
a1=72.7square meters
I've modified your drawing a little bit (see attachment)

1. Someone has written 7.3 m at the slanted edge of the prism. That's definitely wrong.

2. To calculate the length of the slanted edge you have to use Pythagorean theorem. I've indicated the right triangle in question ion green. You are supposed to know why the short leg is 0.55 m. The length of the hypotenuse (that's the slanted edge) is approximately 7.2209 m (the exact value - if the given lengthes are exact! - is $\frac1{20} \sqrt{20857}\ m$)

3. ## Re: trying to calculate the surface area and volume of a prism

The 7.3m value is directly from the text book. This prism was scanned from the book, nothing was altered

4. ## Re: trying to calculate the surface area and volume of a prism

Hello, hotboxdriver!

earboth is correct . . . the slant height is 7.2209...

The measurements seem to be to one decimal place.
. . That's why they rounded 7.2209 up to 7.3.
[The height and the slant height must not both be 7.2, you see.]

The front and back panels are trapezoids:. $h = 7.2,\:b_1 = 4.5,\:b_2 = 5.6$
Each has area: . $\tfrac{7.2}{2}(4.5 + 5.6) \:=\:36.36$
. . Front/Back: . $2 \times 36.36 \:=\:72.72\text{ m}^2$

The side panels are $18.9\!\times\!7.3$ rectangles.
. . Left/Right: . $2 \times 18.9 \times 7.3 \:=\:275.94\text{ m}^2$

The top is a $5.6\!\times\!18.9$ rectangle.
. . Top: . $5.6 \times 18.9 \:=\:105.84\text{ m}^2$

The bottim is a $4.5\!\times\!18.9$ rectangle.
. . Bottom: . $4.5 \times 18.9 \:=\:85.05\text{ m}^2$

The total surface area is:. $539.55\text{ m}^2.$

The volume is the area of a trapezoidal face times the length.

. . $V \;=\;36.36 \times 18.9 \:=\:687.204\text{ m}^3.$