Answer: Total area = 104 + 16√13
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