Find the lateral area of a regular pyramid whose base is a square whose slant height is 5 m, and whose height is 3 m.
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To find the lateral area of a regular pyramid, you need to calculate the area of all the triangular faces that make up the sides of the pyramid.
In this case, we're given that the base of the pyramid is a square, and the slant height (lateral height) is 5 m, while the height (vertical height) is 3 m.
To find the lateral area, we can follow these steps:
1) Find the length of the side of the square base.
Since the base is a square, all sides are equal. So, let's call the side length of the square base "s".
2) Find the area of one of the triangular faces.
The area of a triangle is given by the formula: (base * height) / 2.
In this case, the base of the triangle is the side length of the square base, which is "s".
The height of the triangle can be found using the Pythagorean theorem. The height represents the distance from the apex (top) of the pyramid to the center of one of the sides of the square base.
The height is the hypotenuse of a right triangle, with the slant height (5 m) as one leg, and half of the side length of the square base (s/2) as the other leg.
Using the Pythagorean theorem, we can find the height: height^2 = (slant height)^2 - (s/2)^2.
So, height = sqrt((slant height)^2 - (s/2)^2).
Now, we can calculate the area of one triangular face: (s * height) / 2.
3) Multiply the area of one triangular face by the number of faces (4 for a square base pyramid).
Since the pyramid has a square base, there are 4 triangular faces.
Therefore, to find the lateral area of the pyramid, we need to calculate (s * height) / 2 and multiply it by 4.
Let's go ahead and calculate the lateral area of the pyramid.