The base of the straight triangular prism is a right-angled triangle with legs 6 and 8. The diagonal

| April 23, 2021 | education

The base of the straight triangular prism is a right-angled triangle with legs 6 and 8. The diagonal of the larger side face forms an angle of 45 degrees with the base. Find the volume of the pyramid.

According to the condition of the problem, the base of the prism is a right-angled triangle, the legs of which are known.

Let’s find what the hypotenuse of a given triangle is equal to, using the Pythagorean theorem:

х² = 6² + 8²,

x² = 36 + 64,

x² = 100,

x = 10.

The hypotenuse of the base is the side of the larger face of the prism.

The angle between the side of the face and its diagonal is 45 degrees, that is, the diagonal of the face with the side of the base and the height of the prism form a right-angled isosceles triangle. This means that the height of the prism is 10.

Thus, the volume of the prism is:

V = 10 * (6 * 8) / 2 = 10 * 24 = 240.



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