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babymother [125]
2 years ago
7

I’ll give you brainliest for the first person with an answer

Mathematics
1 answer:
raketka [301]2 years ago
4 0

Answer:

1296mm^2

Step-by-step explanation:

Surface Area of the Rectangular Prism to the left on top of the box:

Area of square = lw, 9mm * 9mm = 81mm, then multiply by 2 because 2 of the squares are a part of the surface, giving <u>162mm^2</u>

Area of a rectangle =lw, 9mm * 9mm = 81mm, then multiply by 2 again, because 2 rectangles are a part of the surface, giving <u>162mm^2</u>

So, the total surface area of the rectangular prism to the left on top, is 324mm^2

Surface Area of the Triangular Prism:

Area of a triangle: 1/2bh, and our base length would be 12, because we have to subtract 9 from 21 since the base length of the triangle isn't stated. Anyways, A = 1/2bh, so A = 1/2(12)(9) = 54mm^2, but multiply by two, so we get <u>108mm^2</u>.

Area of the rectangle: lw, so 15mm * 9mm = <u>135mm^2</u>

So, the total surface area of the triangular prism is 243mm^2

Surface Area of the Rectangular Prism at the bottom:

Area of the long rectangles in front = lw, 21mm * 9mm = 189mm^2, multiply by 2, <u>378mm^2</u>

Area of the rectangles to the side = lw, 9mm * 9mm = 81mm^2, multiply by 2, <u>162mm^2 </u>

Area of the rectangle at the very bottom = lw, 21mm * 9mm = <u>189mm^2</u>

So, the total surface area of the rectangular prism at the bottom is 729mm^2

Add all the total surface areas of each shape to get the total surface area of the figure:

324mm^2 + 243mm^2 + 729mm^2 = 1296mm^2

The surface area of the figure above is 1296mm^2

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