The lateral area of a pyramid is given by the formula:
Lateral area = (1/2) * perimeter of base * slant height
To find the perimeter of the base, we need to know the length of one side of the square base. Since the base measures 8 m, each side of the square base measures:
8 / √2 ≈ 5.66 m
To find the slant height, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle with one leg equal to half the length of a side of the base (since the pyramid is on its side) and the other leg equal to the height of the pyramid. Thus:
slant height = √[(1/2 * 8)^2 + 22^2] ≈ 22.63 m
Now we can plug in these values to find the lateral area:
Lateral area = (1/2) * 4 * 5.66 * 22.63 ≈ 254.5 m^2
Therefore, the lateral area of the square pyramid is approximately 254.5 square meters.
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A pyramid on its side is shown with its height measuring 22 m and its base measuring 8 m.
Find the lateral area of the square pyramid.
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