If I have a square pyramid. Each side of the base has 60m and the height is 20 m. What is the lateral area of pyramid
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To find the lateral area of a square pyramid, you need to calculate the sum of the areas of the four triangular faces.
The formula to find the lateral area of a square pyramid is:
Lateral Area = (Perimeter of base) × (Slant height) / 2
First, let's calculate the perimeter of the base:
Since each side of the square base has a length of 60m, the perimeter of the base would be:
Perimeter = 60m + 60m + 60m + 60m = 240m
Next, we need to calculate the slant height (s). In a right pyramid, the slant height can be found using the Pythagorean theorem, where the slant height (s) is the hypotenuse and the height (h) and half the side length of the base (a/2) are the other two sides:
s = sqrt(h^2 + (a/2)^2)
In this case, the height (h) is given as 20m and the side length of the base (a) is given as 60m. Plugging in the values:
s = sqrt(20m^2 + (60m/2)^2)
s = sqrt(400m^2 + 900m^2)
s = sqrt(1300m^2)
s ≈ 36.06m
Now we can substitute the values into the lateral area formula:
Lateral Area = (Perimeter of base) × (Slant height) / 2
Lateral Area = (240m) × (36.06m) / 2
Lateral Area = 4324.8m^2
Therefore, the lateral area of the square pyramid is approximately 4324.8 square meters.