Question

What is the surface area of the right trapezoidal prism?

Answer 1

Depends. See text.

Explanation:

Surface area or volume?

Ther are two options.

Case 1: we know nothing about the green angles I've marked in green. Data is insufficient to determine the perimeter of the trapezoid base, and then to calculate the surface area.

Case 2:Unlikely, since the right angles are marked everywhere else when not obvious: the base of the prism is a right trapezoid, ie two of the angles measures 90°. In that case we can easily find the length of the missing side with pythagorean theorem:
`l=√(1+3^2)= √(10)`. Perimeter becomes
`2p=6+7+3+√(10)=16+√(10)`. Base area is
`A_b=\frac12(6+7)* 3 = \frac{39}2` And the total surface becomes
`S= 2A_b+2pH = 39+(16+√(10))20 = 39+320+20√(10)=359+20√(10)`

Or is it the volume you want? Way simpler, we calculate the area of the prism (see above) and multiply it by the height of the solid:

`V = A_bH = \frac{39}2* 20 = 390`