Answer:
2064cm²
Step-by-step explanation:
The total surface area of a shape is given by the area of each side. In this case 2 × the trapezium/trapezoid, 1 × the top side, 1 × the bottom side, 1 × the left slanted side and 1 × the right slanted side.
Let's start with the trapeziums/trapezoids. The formula for their area is [tex]\frac{1}{2}[/tex]h(a+b). In this case, because there are 2, we can work them out at once without the [tex]\frac{1}{2}[/tex].
By substituting a with 6cm (the top length), b with 27cm (the bottom length), and h with 8cm (the height), the equation becomes 8(27+6) or 8×33, which can be solved to 264cm².
The rest of the sides are rectangles, which use the formula lw for area. For the top side, this is 6×30, or 180cm².
For the bottom side, this is 27×30, or 810cm².
For the left slanted side, this 10×30, or 300cm².
For the right slanted side, this is 17×30, or 510cm².
We should add these all together to get the final result. This equation is 264+180+810+300+510. This adds up to 2064cm².
**This content involves total surface area of prisms, which you may wish to revise. I'm always happy to help!
