The surface area of the following square pyramid is 152 cm2. What is the slant height, l, of the square pyramid in centimeters? The base is 8cm.
surface area 152cm2
To find the slant height (l) of a square pyramid, we can use the formula:
l² = h² + (0.5b)²
Where:
l = slant height
h = height of the pyramid
b = length of one side of the base
In this case, we are given the surface area of the pyramid (152 cm²) and the length of one side of the base (8 cm). We need to find the slant height (l).
To find the height (h) of the pyramid, we can use the formula:
h = √(l² - (0.5b)²)
Now, let's plug in the given values into the formula and solve the equation step by step.
l² = h² + (0.5b)²
152 = h² + (0.5 * 8)²
152 = h² + 16
Rearranging the equation, we have:
h² = 152 - 16
h² = 136
Taking the square root of both sides, we get:
h = √136
h ≈ 11.66 cm (rounded to two decimal places)
Now, we can use the value of the height to find the slant height:
l = √(h² + (0.5b)²)
l = √(11.66² + (0.5 * 8)²)
l ≈ √(136 + 16)
l ≈ √152
l ≈ 12.33 cm (rounded to two decimal places)
Therefore, the slant height (l) of the square pyramid is approximately 12.33 cm.