Question

Find the surface area of the composite figure​

Answer 1

9514 1404 393

Answer:

  224 in²

Step-by-step explanation:

There are a couple of ways to go at this. Here, we choose to figure the areas of each of the prisms individually, then subtract the "hidden" area where they are joined together.

The area of a prism is ...

  A = 2(LW +H(L+W))

Pink area:

  A = 2(10·4 +2(10+4)) = 2(40 +28) = 136 . . . square inches

Green area:

  A = 2(7·4 +4(7+4)) = 2(28 +44) = 144 . . . square inches

One 4 in × 7 in face of the green prism meets with a similar area of the pink prism, so the area hidden at that interface is 2(4·7) = 56 square inches. Then the total surface area of the composite figure is ...

  SA = 136 in² +144 in² -56 in² = 224 in²

Answer 2

Answer:

$=280$ $in^2$

Step-by-step explanation:

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Let's find the surface area of the pink rectangular prism first.

$2*10=20+20=40$

$4*10=40+40=80$

$4*2=8+8=16$

$40+80+16=136$

The surface area for the pink rectangular prism is $136$ $in^2$.

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Now, let's find the surface area of the green rectangular prism.

$4*7=28+28=56$

$4*7=28+28=56$

$4*4=16+16=32$

$56+56+32=144$

The surface area for the green rectangular prism is 144 $in^2$.

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Now let's add the surface area of both rectangular prisms to find the surface area of the composite figure.

$136+144=$

$=280$ $in^2$

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Hope this is helpful.