Total surface area is sum of area of all parts of surface. The surface area of the box is 34 squared feet.
How to find the area of surface of a figure if its split in parts?
The area of surface of a figure is sum of area of all sub-parts of it. It is because we want to get the total area of its surface.
For the given case, the box given has:
- Area of top = Area of bottom
- Area of back = Area of front
- Area of left side = Area of right side.
(its all because of assuming box is cuboid or say rectangular prism)
Thus,
Surface area of box = twice of (area of top + area + left side + area of back)
Calculating these sub areas:
Area of top = [tex]2 \times 4 = 8 \: \rm ft^2[/tex]
Area of back = [tex]1\dfrac{1}{2} \times 4 = \dfrac{2+1}{2} \times 4 = 6 \: \rm ft^2[/tex]
Area of left side: [tex]1\dfrac{1}{2} \times 2 = \dfrac{2+1}{2} \times 2 = 3 \: \rm ft^2[/tex]
Thus,
Surface area of box = [tex]2(8 + 6 + 3) = 2 \times 17 = 34 \: \rm ft^2[/tex]
Thus,
The surface area of the box is 34 squared feet.
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