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.?
*, 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)
◎ 372ft.
O 57.3 ft.
• 9.3 ft.
• 6.5 ft.
To find the height of the base, we can use the formula for the surface area of a regular triangular pyramid, which is given by:
Surface Area = (1/2) * base perimeter * slant height + base area
From the given information, we know that the base perimeter is 6 ft and the slant height is 8 ft. Let's substitute these values into the formula:
100 = (1/2) * 6 * 8 + base area
Simplifying further:
100 = 24 + base area
Now, let's subtract 24 from both sides:
base area = 100 - 24
base area = 76 ft²
We can find the height of the base by using the formula for the area of an equilateral triangle, which is given by:
Area = (sqrt(3)/4) * base length²
From the given information, we know that the base length is 6 ft. Let's substitute this into the formula:
76 = (sqrt(3)/4) * 6²
Simplifying further:
76 = (sqrt(3)/4) * 36
76 = (sqrt(3)/4) * 6 * 6
To isolate the height, we'll divide both sides by (sqrt(3)/4) * 6:
76/((sqrt(3)/4) * 6) = 6
Approximately solving this expression using a calculator, we get:
Height of the base ≈ 6.5 ft.
Therefore, the height of the base to the nearest tenth is 6.5 ft.