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The net of a composite space figure is shown below.
A. What figures make up the composite space figure?
B. What is the surface area of the composite space figure? Round your answer to the
nearest square centimeter.

The net of a composite space figure is shown below A What figures make up the composite space figure B What is the surface area of the composite space figure Ro class=

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sylvain96

Answer:

A. What figures?: Hexagonal prism topped by a hexagonal cone

B. 246 sq cm

Step-by-step explanation:

A. What figures?

Imagine you're rolling up all 6 vertical pointy pieces around the base hexagon.  Then you'll have like a crown top with all the triangles.  You can fold these triangles to have their tips meet and form a hexagonal cone...

So, you'll have a hexagonal prism, topped with a hexagonal cone.

B. Surface area.

That's just a matter of calculating the areas of all triangles, rectangles and hexagon of the assembly.

Triangles: base: 4 cm, height: 5 cm, quantity: 6

A = (b * h) / 2 = (4 * 5) / 2 = 10 sq cm

AT = 6 * V = 6 * 10 = 60 sq cm

Rectangles: base: 4 cm, height: 6 cm, quantity: 6

A = b * h = 4 * 6 = 24 sq cm

AR = 6 * V = 6 * 24 = 144 sq cm

Hexagon: side: 4 cm, quantity: 1

Since it's a regular hexagon and we know its side length...

AH =  (3√3 * s²)/2 = (3√3 * 16)/2 = 24√3 = 41.57 sq cm

Then we add everything together:

A = AT + AR + AH

A = 60 + 144 + 41.57 = 245.57 sq cm

Rounded answer: 246 sq cm

MathPhys

Answer:

246 cm²

Step-by-step explanation:

The composite space figure consists of:

  • One hexagon (side length 4 cm)
  • Six rectangles (4 cm x 6 cm)
  • Six triangles (base 4 cm, height 5 cm)

The surface area is the sum of all the areas of each figure.

Area of a hexagon = ½√(27) s²

Area of a rectangle = wl

Area of a triangle = ½ bh

So the total area is:

A = ½ √(27) (4)² + 6(4×6) + 6(½×4×5)

A = 8√(27) + 204

A ≈ 246 cm²

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