Answer :

mhanifa

Answer:

  • S = 24√3 + 48√2

Step-by-step explanation:

Area of the base:

  • A = aP/2
  • A = 2√3(6*4)/2 = 24√3

Height of triangle faces:

  • h = √l² - (b/2)² = √6²-(4/2)² = √32 = 4√2

Area of triangle faces:

  • A = 6(bh/2) = 3bh
  • A = 3(4)(4√2) = 48√2

Total surface area:

  • S = 24√3 + 48√2
  • Your answer is right
semsee45

Answer:

Surface Area = (24√3 + 28√2)  ft²

Step-by-step explanation:

A hexagonal pyramid comprises:

  • hexagonal base
  • 6 congruent isosceles triangles

Area of a Regular Polygon

[tex]\textsf{A}=\sf \dfrac{n\:s\:a}{2}[/tex]

where:

  • n = number of sides
  • s = length of one side
  • a = apothem (the line drawn from the center of any polygon to the midpoint of one of the sides)

From inspection of the diagram:

  • n = 6 (hexagon)
  • s = 4 ft
  • a = 2√3 ft

Substitute the given values into the formula to find the area of the hexagonal base:

[tex]\implies \sf A=\dfrac{6 \cdot 4 \cdot 2\sqrt{3}}{2}[/tex]

[tex]\implies \sf A=24 \sqrt{3}\:\:ft^2[/tex]

Area of an isosceles triangle

[tex]\sf A=\dfrac{1}{2}\left(b\sqrt{a^2-\dfrac{b^2}{4}}\right)[/tex]

where:

  • a = length of the equal sides
  • b = length of the base

From inspection of the diagram:

  • a = 6 ft
  • b = 4 ft

Substitute the given values into the formula to find the area of one of the triangles:

[tex]\implies \sf A=\dfrac{1}{2}\left(4\sqrt{6^2-\dfrac{4^2}{4}}\right)[/tex]

[tex]\implies \sf A=\dfrac{1}{2}\left(4\sqrt{32}\right)[/tex]

[tex]\implies \sf A=8\sqrt{2}\:\:ft^2[/tex]

Surface Area of the Hexagonal Prism

[tex]\implies \sf SA=\textsf{Area of hexagonal base}+6 \times \textsf{Area of isosceles triangle}[/tex]

[tex]\implies \sf SA=24\sqrt{3}+6(8\sqrt{2})[/tex]

[tex]\implies \sf SA=24\sqrt{3}+48\sqrt{2}\:\:ft^2[/tex]

Learn more about areas of regular polygons here:

https://brainly.com/question/27949277

Learn more about surface areas of prisms here:

https://brainly.com/question/27708763

Other Questions