How do you work out the surface area of a prism which has a cross section of a trapezium?

Question

How do you work out the surface area of a prism with a cross section of a trapezium?

Answer 1

Volume:
Work out the area of the trapezium then multiply by the length of the prism.

Area of a trapezium= (a+b)h/2 where a and b are the two parallel sides and h is the perpendicular distance between them.
Area :
Find the areas of the two end trapezia.
Then find tha areas of the top,side(s) and bottom rectangles.
To find the length of one of the sloping sides you will have to use pythagoras' theorem.
it is difficult to explain without a diagram (draw your own)
let the sloping side be x.

x squared = (b-a) squared + h squared.
I hope you can get it from this

Answer 2

First find the area of the trapezium using the formula:

1/2(a+b) * height

((Note: a and b are the lengths of the parallel sides))

Multiply the answer you get by 2 to get the area of two sides.
Let this answer equal x



Next to find the area of the other sides:

Add up all the sides of the trapezium and multiply by the prism's height, NOT by the height of the trapezium.
Let this answer be y


Then add the answer you got in section one and two and there you have it, the surface area.

Total surface area = x + y

Answer 3

Simple.
Find the length of each side of the trapezium and add them together. Then multiply by the length of the prism and add the area of the trapezium twice (i.e for both sides of the prism).
Hope it helps!!

Answer 4

Let a be one of the two parallel bases, and
let b be the other parallel base of the trapezium/trapezoid, and
let h be the perpendiculr distance between a and b.
Then the area of the the upper and kower bases of the prism wili each be [(a+b)h]/2 so their combined area is (a+b)h.

The lateral area will have consist of four faces which are all rectangles. One will have an area of ax and one will have an area of bx, where x is the altitude of the prism. The other two faces will have areas of x*s1 + x*s2, where s1 and s2 cannot be determined without further information.

Total area is (a+b)h + ax+bx +s1x +s2x, or
Total area = (a+b)h + px where p is the perimeter of the trapezoid.

Answer 5

A cross section is what you get when you cut the shape in some particular way. In this case it means that if you look at the bath from one of its endpoints you will see a trapezium.

Answer 6

u will have 2 trapeziums with area
Where l is the lenght
h is the perpendicular height
a is the lenght ofone of the parallel sides
b is the lenght of the other parallel side

(a+b)h /2

one rectangle with area
a*l

one rectangle with area

b*l

and 2 rectangles with area

((((b-a)/2)^2 +h^2)^.5)*l

So over all
(a+b)h + al + bl + ((((b-a)/2)^2 +h^2)^.5)*l