Answer:
- 18 cm
- 3 cm
- 9√3 cm²
- (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
