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If the sides of a regular triangular pyramid are right triangles and the length of its bottom side is a, then its total area is?
From the side length of the equilateral triangle on the bottom as a, we can get three edge lengths as a √ 2 / 2, side area = 3 * 1 / 2 * a √ 2 / 2 * a √ 2 / 2 = 3 / 4 * a ^ 2, bottom area = 1 / 2 * a * √ 3 * a = √ 3 / 2 * a ^ 2, total area = 3 / 4 * a ^ 2 + √ 3 / 2 * a ^ 2 = ((3 + 2 √ 3) / 4 * a ^ 2
The sides of a regular triangular pyramid are all right triangles, and the bottom length is a to find its surface area
The area of equilateral triangle on the bottom is: (√ 3 / 4) a ^ 2, and the side edge is: √ 2 / 2A,
Side area = 3 * (√ 2 / 2a) ^ 2 / 2 = 3A ^ 2 / 4,
Surface area = (√ 3 / 4) a ^ 2 + 3A ^ 2 / 4 = (3 + √ 3) a ^ 2 / 4
The side areas of a regular triangular pyramid are all right triangles, and the side length of its bottom is 2A
The edges of a regular triangular pyramid are equal, so its side is an isosceles right triangle, and its oblique side is 2A long,
So the right angle side length is 2A / √ 2 = √ 2a, and the area of each side is 1 / 2 * √ 2A * √ 2A = a ^ 2
Side area = 3A ^ 2
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