To find the surface area of an equilateral triangular pyramid, we first need to calculate the area of the three triangular faces and the base.
Given that the lateral edge is 15cm and the slant height is 9cm, we can use the Pythagorean theorem to find the height of the triangle.
The height (h) can be calculated as:
h = sqrt(9^2 - (15/2)^2)
h = sqrt(81 - 56.25)
h = sqrt(24.75)
h ≈ 4.975 cm
Now, we can find the area of one of the triangular faces using the formula:
Area = (1/2) * base * height
Area = (1/2) * 15 * 4.975
Area = 37.3125 cm²
Since the pyramid is equilateral, all three triangular faces have the same area.
Therefore, the total area of all three triangular faces is 3 * 37.3125 = 111.9375 cm².
The area of the base can be calculated using the formula for the area of an equilateral triangle:
Area = (sqrt(3)/4) * side^2
Area = (sqrt(3)/4) * 15^2
Area = (sqrt(3)/4) * 225
Area ≈ 97.43 cm²
Finally, the total surface area of the equilateral triangular pyramid is the sum of the areas of the three triangular faces and the base:
Surface area = 111.9375 + 97.43
Surface area ≈ 209.3675 cm²
Therefore, the surface area of an equilateral triangular pyramid with a lateral edge of 15cm and a slant height of 9cm is approximately 209.3675 cm².
Find the surface area of an equilateral triangular pyramid if lateral edge is 15cm and the slant height is 9cm.
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