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1) What is the perimeter (P) of the base of the pyramid?

2) What is the slant height (l) of the pyramid?

3) What is the area of the base (B)?

4) What is the surface area (SA = B + 1/2 Pl)?

1 What is the perimeter P of the base of the pyramid 2 What is the slant height l of the pyramid 3 What is the area of the base B 4 What is the surface area SA class=

Respuesta :

sqdancefan

Answer:

  1. 18 cm
  2. 3 cm
  3. 9√3 cm²
  4. (27 +9√3) cm² ≈ 42.49 cm²

Step-by-step explanation:

You want the perimeter, slant height, base area, and total surface area of a pyramid with an equilateral triangle base and isosceles right triangle faces, given a base edge length of 6 cm.

1) Perimeter

The perimeter is the sum of the lengths of the base edges. The three edges are the same length, so the perimeter is ...

  P = 3s = 3(6 cm)

  P = 18 cm

2) Slang height

The slant height is the altitude to the hypotenuse of an isosceles right triangle with hypotenuse 6 cm. That altitude is half the length of the hypotenuse:

  l = (6 cm)/2

  l = 3 cm

3) Base area

The area of the base is given by ...

  B = (√3)/4·s² . . . . . where s is the side length of the equilateral triangle

  B = (√3)/4·(6 cm)²

  B = 9√3 cm²

4) Surface area

The surface area formula is given as ...

  SA = B +1/2Pl

  SA = 9√3 +1/2(18)(3) . . . . . cm²

  SA = 27 +9√3 cm² ≈ 42.49 cm²

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