Question

Find the lateral surface area of the triangular pyramid with an equal lateral base represented by the ten meters

Answer 1

The lateral surface area of a triangular pyramid can be calculated using the formula:

Lateral Surface Area = 0.5 * perimeter of base * slant height

Since the lateral base is an equilateral triangle, each side is equal to 10 meters. Therefore, the perimeter of the base can be calculated as:

Perimeter of base = 3 * side length = 3 * 10 = 30 meters

Next, we need to determine the slant height of the pyramid. This can be calculated using the Pythagorean theorem. The slant height (l) can be found using the formula:

l = sqrt(h^2 + (0.5 * side length)^2)

Since the base is an equilateral triangle, the height of the triangle (h) can be calculated using:

h = sqrt(side length^2 - (0.5 * side length)^2) = sqrt(10^2 - (0.5 * 10)^2) = sqrt(100 - 25) = sqrt(75) = 5 * sqrt(3)

Now, we can calculate the slant height:

l = sqrt((5 * sqrt(3))^2 + (0.5 * 10)^2) = sqrt(75 + 25) = sqrt(100) = 10 meters

Finally, we can calculate the lateral surface area:

Lateral Surface Area = 0.5 * 30 * 10 = 150 square meters

Therefore, the lateral surface area of the triangular pyramid with an equal lateral base of 10 meters is 150 square meters.