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Find the total area for the prism.104+ 16 13102 +15√1396+12/1389+6√13

Find the total area for the prism.104+ 16 13102 +15√1396+12/1389+6√13-example-1
User Marko Jurisic
by
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1 Answer

20 votes
20 votes

Answer: Total area = 104 + 16√13

Step-by-step explanation:

The total area is the sum of the area of each face. From the figure, the faces are

2 similar triangular faces

smaller rectangular face on the left

one rectangular face at the back

one rectangular face at the front

Considering the triangles,

area = 1/2 x base x height

From the diagram,

height = 6

base = 4

Area of 2 triangular faces = 2 x 1/2 x 4 x 6 = 24

Considering the smaller rectangular face on the left,

length = 8

width = 4

Area = 8 x 4 = 32

Considering the bigger rectangular face at the back,

length = 8

width = 6

Area = 8 x 6 = 48

Considering the bigger rectangular face at the front,

length = 8

We would find the width by applying the pythagorean theorem which is expressed as

hypotenuse^2 = one leg^2 + other leg^2

hypotenuse = width

one leg = 6

other leg = 4

width^2 = 6^2 + 4^2 = 52

width = √52 = 2√13

Area 8 x 2√13 = 16√13

Thus,

Total area = 24 + 32 + 48 + 16√13

Total area = 104 + 16√13

User Stackex
by
2.7k points