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Area of top triangle = [tex]\frac{b \cdot h}{2} = \frac{4 \cdot 3}{2} = \frac{12}{2} = 6[/tex]

Area of bottom triangle = Area of top triangle = [tex]6[/tex]

Area of left rectangle = [tex]l \cdot w = 6 \cdot 4 = 24[/tex]

Area of middle rectangle = [tex]l \cdot w = 6 \cdot 5 = 30[/tex]

Area of right rectangle = [tex]l \cdot w = 6 \cdot 3 = 18[/tex]

Area of polyhedron = top triangle + bottom triangle + left rectangle + middle rectangle + right rectangle = [tex]6 + 6 + 24 + 30 + 18 = 84[/tex]

Surface area the given polyhedron is equals to 84square units.

What is surface area?

"Surface area is the total area of all the surfaces occupied by any three dimensional body."

Formula used

Area of right angled triangle = ( 1/2) × base ×height

Area of rectangle = length ×width

According to the question,

As per the given diagram,

Two right triangles with equal measurement

Base = 4units

height = 3 units

Hypotenuse = 5units

Substitute the value in the formula we get

Area of 1 right angled triangle = ( 1/ 2) × 4 × 3

                                                  = 6 square units

Therefore,

Area of 2 right angled triangle = 2 × 6

                                                  = 12 square units                             ___(1)

Rectangle 1

Length = 6units

width = 4 units

Area of rectangle 1 = 6 × 4

                                = 24 square units                                             ___( 2)

 

Rectangle 2

Length = 6units

width = 5 units

Area of rectangle 2 = 6 × 5

                                = 30 square units                                        _____(3)

Rectangle 3

Length = 6units

width = 3 units

Area of rectangle 3 = 6 × 3

                                = 18 square units                                             ___( 4)

Add(1) ,(2) , (3) , and (4), we get

Surface area of the polyhedron = 12 +24 +30 +18

                                                      = 84 square units

Hence, surface area the given polyhedron is equals to 84square units.

Learn more about surface area here

https://brainly.com/question/2835293

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