The base of a straight triangular prism is a right-angled triangle with an acute angle of 60 ° and a leg adjacent

The base of a straight triangular prism is a right-angled triangle with an acute angle of 60 ° and a leg adjacent to this angle, equal to 9 cm. Height 20cm, find the volume of the prism, square the full surface?

1. The volume of the prism is equal to the product of the area of ​​the base by the height, which means that to find it with a known value of the height, it is necessary to determine the area of ​​the right-angled triangle lying at the base.

2. The area of ​​the base S is calculated by the formula

S = 1/2 * a * b.

The unknown leg b is determined from the formula tg 60 °, its value according to the table is √3.

b: a = tg 60 °; whence b = a * tg60 ° = 9 * √3.

Therefore, S = 1/2 * 9 * 9 * √3 = 81 √3: 2 = 40.5 √3 = 40.5 * 1.73 = 70.

Find the volume V of the prism

V = S * h = 40.5 √3 * 20 = 810 √3 = 810 * 1.73 = 1401.

3. Total surface area S total = 2 * S + (a + b + c) * h.

The hypotenuse from the base triangle is

c = √a + b = √9² + (9 √3) ² = √323 = 18.

Full = 2 * 70 + (9 + 15.6 + 18) * 20 = 140 + 852 = 992.

Answer: V = 1401, S full = 992.