What is the lateral area of a pyramid whose base is a square with sides measuring 16 meters and with a slant height of 17 meters?

each face is a triangle with base 16, altitude 17.

So, 4 * 1/2 * 16 * 17 = 544

To find the lateral area of a pyramid, we need to calculate the sum of the areas of all its triangular faces.

Since the base of the pyramid is a square, each face of the pyramid is actually an isosceles triangle. The slant height is given as 17 meters.

We can find the height of the triangle by using the Pythagorean theorem:
h^2 = slant height^2 - base length/2^2
h^2 = 17^2 - 8^2
h^2 = 289 - 64
h^2 = 225
h = √225
h = 15 meters

Now, we can find the area of one triangular face using the formula for the area of a triangle:
area = 0.5 * base length * height
area = 0.5 * 16 * 15
area = 120 square meters

Since there are four triangular faces on the pyramid (one for each side of the square base), the total lateral area is:
lateral area = 4 * area
lateral area = 4 * 120
lateral area = 480 square meters

Therefore, the lateral area of the pyramid is 480 square meters.

To find the lateral area of a pyramid, we need to find the sum of the areas of all the triangular faces. The formula for the lateral area of a pyramid is given by:

Lateral Area = (1/2) × Perimeter of Base × Slant Height

In this case, the base of the pyramid is a square with sides measuring 16 meters. To find the perimeter of the square, we can multiply the length of one side by 4:

Perimeter of Base = 16 × 4 = 64 meters

Substituting the values into the formula, we have:

Lateral Area = (1/2) × 64 meters × 17 meters

Multiplying these values together, we find:

Lateral Area = 544 meters²

Therefore, the lateral area of the pyramid is 544 square meters.