The side edges of a regular triangular pyramid are mutually perpendicular, and their lengths

| June 19, 2021 | education

The side edges of a regular triangular pyramid are mutually perpendicular, and their lengths are 10.15 and 9 cm. Find the volume of the pyramid.

Triangular pyramid;

The lateral ribs are mutually perpendicular;

Rib length = 10, 15 and 9 cm.

Let’s find the volume of the pyramid.

1) Since the edges are mutually perpendicular, it means that a right-angled triangle lies at the base.

Let the legs of a right-angled triangle be 10 cm and 15 cm, then 9 cm is the height of the triangular pyramid.

2) Find the area of ​​the base, that is, the area of ​​a right-angled triangle. It is equal to half the product of the legs.

S = 1/2 * 10 * 15 = 5 * 15 = 5 * 10 + 5 * 5 = 50 + 25 = 75 cm ^ 2;

3) Find the volume of the triangular pyramid by the formula:

V = 1/3 * S * h = 1/3 * 75 * 9 = 3 * 75 = 3 * 70 + 3 * 5 = 210 + 15 = 225 cm ^ 3.



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