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Find the surface area of the composite figure

Find the surface area of the composite figure-example-1
User Lesya Makhova
by
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1 Answer

26 votes
26 votes

Answer:

268 cm²

Explanation:

You want the surface area of the composite figure consisting of two stacked cuboids.

Composition

The area of the top of the figure is equivalent to the area of the bottom of the figure. The fact that a 2 cm square has been elevated by 6 cm does not change its area.

The lateral area of the magenta cuboid will be added to the total surface area of the green cuboid.

Green cuboid area (including the top 2 cm square):

A = 2(LW + H(L +W)) = 2(4·5 + 10(4 +5)) cm² = 220 cm²

Magenta lateral area

This is the perimeter of the top square, multiplied by the height of the prism:

4(2 cm)(6 cm) = 48 cm²

Total surface area

The total area is the sum of the areas of the parts:

220 cm² + 48 cm² = 268 cm²

SA = 268 cm²

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Additional comment

You could subtract the area of the 2 cm square from the total surface area of the top cuboid. Similarly, you'd have to subtract the area of that square from the area of the top of the green cuboid. Thus, the SA could be found using the formulas for total surface area of each figure.

Doing that adds the area of the 2 cm square three times and subtracts it twice. That's some extra work that we avoided.

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User Yexo
by
2.7k points