Niko has an outdoor play tent in the form of a regular triangular pyramid, covered in fabric on all four sides. The surface area of the tent is 100 ft. squared, the base is 6 ft., and the slant height is 8 ft. What is the height of the base to the nearest tenth?(1 point)
Responses
We can find the height of the base by using the formula for the surface area of a regular triangular pyramid:
Surface Area = (base × height)/2 + 3 (base × slant height)/2
Plugging in the given values, we get:
100 = (6 × height)/2 + 3 (6 × 8)/2
Simplifying the expression, we have:
100 = 3 × height/2 + 3 × 24/2
100 = 3 × height/2 + 3 × 12
100 = 3 × height/2 + 36
Now, we can isolate the height:
3 × height/2 = 100 - 36
3 × height/2 = 64
height/2 = 64/3
height = (64/3) * 2
height = 128/3
height ≈ 42.7
Therefore, the height of the base is approximately 42.7 ft to the nearest tenth.