Question

Use the right triangular prism to find the total surface area of the prism. Leave label off answer.

Answer 1

Step-by-step explanation:

the total surface area is the sum of the 5 individual areas in the surface :

2 triangle sides (left and right).

1 back rectangle side

1 rectangle floor

1 inclined rectangle front side

to get the length of the baseline (Hypotenuse) of the right-angled triangles on the side. we use Pythagoras

c² = a² + b²

where c is the Hypotenuse (the side opposite of the 90° angle).

c² = 3² + 4² = 9 + 16 = 25

c = 5

so, now, we have everything we need.

the area of a triangle side (since it is right-angled) :

4×3/2 = 6

2 sides, that makes 12

the area of the back side

6×3 = 18

the area of the floor

6×4 = 24

the area of the inclined front side

6×5 = 30

so, the total surface area is

12+18+24+30 = 84