all edges of asquare pyramid are equal.heidht of pyramid is 8root2.find length of base edge and lateral surface area?
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Let each edge of the square pyramid be = a units.
The diagonal on the square base = a√2 units
Half diagonal = a / √2 units
One lateral edge, half diagonal and the altitude (height) are in a right angle triangle.
a² = (a/√2)² + (8√2)²
a²/2 = 128
a = 16 units.
Each of the four lateral surfaces are all equilateral triangles.
So area of one face = 1/2 * √3/2 a * a = √3/4 * 256 = 110.85 square units.
Total lateral surface area = 443.40 sq units
The diagonal on the square base = a√2 units
Half diagonal = a / √2 units
One lateral edge, half diagonal and the altitude (height) are in a right angle triangle.
a² = (a/√2)² + (8√2)²
a²/2 = 128
a = 16 units.
Each of the four lateral surfaces are all equilateral triangles.
So area of one face = 1/2 * √3/2 a * a = √3/4 * 256 = 110.85 square units.
Total lateral surface area = 443.40 sq units
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