The base of a straight prism is a right-angled triangle with a hypotenuse of 10 cm and a leg of 6 cm

The base of a straight prism is a right-angled triangle with a hypotenuse of 10 cm and a leg of 6 cm, and the lateral edge of the prism is 5 cm. Find the lateral surface area and volume of the prism.

Suppose that at the base of the straight prism lies a right-angled triangle ABC with a hypotenuse AB = 10 cm and a leg AC = 6 cm, then we find the second leg using the Pythagorean theorem:
AB² = AC² + BC² or
10² = 6² + ВС², we get
BC = 8 cm.
From the condition of the problem it is known that the lateral edge of the prism is AD = h = 5 cm. The area of ​​the lateral surface of the straight prism S is found by the formula S = Pb ∙ h, where Pb is the base perimeter and Pb = AB + AC + SV, h is the height of the prism. Substitute the values ​​of the quantities into the formula and perform the calculations:
S = (10 + 6 + 8) ∙ 5;
S = 120 cm².
The volume of the straight prism V is found by the formula V = Sbase ∙ h, where Sbase is the area of ​​the base and Sbase = (АС ∙ ВС): 2.
Substitute the values ​​of the quantities into the formula and perform the calculations:
V = (6 ∙ 8): 2 ∙ 5;
V = 120 cm³.
Answer: the area of ​​the lateral surface of a straight prism is 120 cm², and the volume of the prism is 120 cm³.