At the base of the pyramid lies a right-angled triangle whose legs are 3cm and 4cm. All side ribs are equal.

| March 10, 2021 | education

At the base of the pyramid lies a right-angled triangle whose legs are 3cm and 4cm. All side ribs are equal. The height of the pyramid is 6cm. Find the side edge and total surface area of the pyramid.

If all three sides of the pyramid are equal, then their projections onto the base are also equal. The length of the projections in this case will be equal to the radius of the circumscribed circle, and the point of their intersection will be in the center of the circle. Triangle ABC is rectangular, so the center of the circumscribed circle will be in the middle of the hypotenuse at point O. Find the length of the hypotenuse:

AC = √ (AB ^ 2 + BC ^ 2) = √ (3 ^ 2 + 4 ^ 2) = 5. Half of the hypotenuse (and the length of the edge projection):

ОА = ОB = OC = 5/2 = 2.5 cm.

The length of the edge AS is found as the hypotenuse of the right-angled triangle AOS:

l = √ (AO ^ 2 + OS ^ 2) = √ (2.5 ^ 2 + 6 ^ 2) = √42.25 = 6.5 cm.

Answer: 42.86 cm2.



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