Find the surface area
please show work

Step-by-step explanation:

The pentagon faces are made up of five triangle each with 9 ft bases and 6.2 ft heights. And there are five rectangular sides of 9 by 5 feet. So the total surface area is

A=2*5*9*6.2/2+5*9*5

A=279+225

A=504 ft^2

Formula: nl(b + h) it is derived as well

504 ft²

Step-by-step explanation:

Each vertical face is a rectangle.

Area of each face = length x breadth = lb

For n-sided polygon, area of vertical faces = n x lb = nlb

For horizontal faces:

Observe: you can actually divide that face in 5 right-angled triangle(two edge point & centre form right angled ∆). [For n-sided, that's n right angled ∆]

For 2 such faces, you have 2 x n times of area of 1 ∆.

Area of 2n∆ = 2n( ½ x h x base(length)) = nhl

Total area = area of horizontal surfaces + area of vertical surfaces

Total area = nlb + nhl = nl(b + h)

Total area = 5*9(5 + 6.2) = 504 ft²

step-by-step explanation:

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