Question

How much metal did they use to cover the ramp, including the bottom?

Answer 1

Answer:  1.79 square meters

Work Shown:

A = area of the triangular front face

A = base*height/2

A = 0.8*0.1/2

A = 0.04

L = lateral surface area

L = combined area of all the rectangular faces

L = (perimeter of the triangular face)*(depth of the prism)

L = (0.1+0.8+0.81)*(1)

L = 1.71

SA = total surface area of the triangular prism

SA = 2*A+L

SA = 2*0.04+1.71

SA = 1.79 square meters

Answer 2

Answer:

1.79 m²

Step-by-step explanation:

the other answer is correct.

that approach works, because it is a regular prism with equal heights and equal depths along the whole object.

in general you need to add all individual surface areas.

in our case here we have 5 of them :

top and bottom rectangles

front and back side triangles

left side rectangle

so, the top rectangle is

1×0.81 = 0.81 m²

the bottom rectangle is

1×0.8 = 0.8 m²

a single triangle is

0.1×0.8/2 = 0.04 m²

so, front and back triangles are

2×0.04 = 0.08 m²

the left side rectangle is

0.1×1 = 0.1 m²

so, the whole surface area is

0.81 + 0.8 + 0.08 + 0.1 = 1.79 m²

of course, it is the same result (as I said, the other answer is correct too), but this shows the more general approach for other, more general prisms.