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I need help on how to find a surface area! I will send the full photo!

I need help on how to find a surface area! I will send the full photo!-example-1
User Zhenya
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1 Answer

17 votes
17 votes

we are asked to determine the surface area of the figure. To do that we need to find the areas of each face and add them together. The front face is a trapezoid, and its area is:


A_(tz)=(b+B)/(2)h

Where "b" is the upper base, "B" is the lower base and "h" is the height. Replacing the values:


A_(tz)=(9ft+4ft)/(2)*4.3ft

Solving the operations:


A_(tz)=28ft^2

the upper face is a rectangle, its area is the product of its side:


A_(uf)=(10ft)(9ft)=90ft^2

The area of the lower face is also a rectangle, therefore its area is:


A_(lf)=(4ft)(10ft)=40ft^2

The side face is also a rectangle, and its area is:


A_(sf)=(5ft)(10ft)=50ft^2

Now we add the areas having into account that the front and side faces repeat themselves. the total surface area is:


A=2A_(tz)+A_(uf)+A_(lf)+2A_(sf)

replacing the values:


A=2(28ft^2)+(90ft^2)+(40ft^2)+2(50ft^2)

Solving the operations:


A=286ft^2

Therefore, the surface area is 286 square feet.

User Shannakay
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