Question

Please help!!! Work out the surface area for this solid prism.

Answer 1

3060
`cm^(2)`

Explanation:

Find the cross-sectional area first of the trapezium

`(1)/(2) (a+b)h`

So,
`(1)/(2)(6+34)15`

which is 40 / 2 x 15 = 20 x 15 = 300
`cm^(2)`

Since there are 2 trapeziums (on the front and back): 300 x 2 = 600
`cm^(2)`

Find the Area of the Rectangles

The first rectangle on the top would be: 6x30 = 180
`cm^(2)`

The slanted rectangle on the right would be: 25x30 = 750
`cm^(2)`

The rectangle on the bottom would be: 30x34 = 1020
`cm^(2)`

The hidden rectangle on the left would be: 17 x 30 = 510
`cm^(2)`

So by combining all these calculations, you will get the total surface area which is:

600 + 180 + 750 + 1020 + 510 = 780 + 1770 + 510 = 2550 + 510 = 3060
`cm^(2)`