How do you Find the lateral area of a square pyramid. base:8
Height:22. and side:8 Help pls
To find the lateral area of a square pyramid, you need to calculate the sum of the areas of all four triangular faces.
The formula for the lateral area of a pyramid is: Lateral area = (Perimeter of base) × (slant height) / 2.
To find the perimeter of the base of the square pyramid, since all sides of the base are equal, you can multiply the side length by 4.
Given that the side length is 8, the perimeter of the base will be 8 × 4 = 32.
To find the slant height, you can use the Pythagorean theorem. In a right triangle formed by the height, half the side length of the base, and the slant height, the height is the legs of the right triangle, and the slant height is the hypotenuse.
Using the Pythagorean theorem: slant height = sqrt((base/2)^2 + height^2).
Given that the base is 8 and the height is 22, the slant height will be sqrt((8/2)^2 + 22^2) = sqrt(16 + 484) = sqrt(500) = 10√5.
Finally, substitute the values into the formula for the lateral area of a pyramid: Lateral area = (32) × (10√5) / 2 = 16 × 10√5 = 160√5.
Therefore, the lateral area of the square pyramid is 160√5 square units.