The base of the straight prism is a triangle, in which the sides are 5 cm and 6 cm

| February 6, 2021 | education

The base of the straight prism is a triangle, in which the sides are 5 cm and 6 cm, form an angle of 30 °, and the lateral edge is 4 cm. Find the volume of the prism.

The volume of the prism is equal to the product of the area of the base of the prism by the height of this prism. In the form of a formula, it looks like this: v = s * h, where v is the volume of the prism, s is the area of the base of the prism,
h is the height of the prism. Since, according to the specification, the base of the prism is a triangle, you need to calculate the area of the triangle. According to the known data of the problem, the formula for finding the area of a triangle on two sides and the angle between them is suitable for us. The formula looks like this: s = 1/2 a * b * sin angle.
Decision:
1) s base = 1/2 * 5 * 6 * sin 30.S = 1/2 * 5 * 6 * 0.5 = 7.5. 2) v = 7.5 * 4. V = 30.
The answer is the volume of the prism = 30 cm cubic.



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