Shape and Space 9
3 marks · EasyA triangular prism has a right-angled triangle as its cross-section with side lengths 5 cm, 12 cm and 13 cm. The prism is 8 cm long.
Calculate the length of the diagonal joining one vertex at the base to the opposite vertex at the top, across the full length of the prism.
Find, to 1 decimal place, the angle that this diagonal makes with the base of the prism.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 15.3 cm
(b) 53.5 degrees
Common mistakes: Using prism length instead of side; Forgetting to find angle with correct side
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correct method for finding diagonal using Pythagoras in 3D
A1 (a) · 1 mark · Accurate calculation of the diagonal (15.3 cm, 1 d.p.)
A2 (b) · 1 mark · Angle correct to 1 d.p. (53.5°)
Worked solution
a) Use Pythagoras’ theorem in 3D: diagonal^2 = base^2 + height^2 + length^2 = 5^2 + 12^2 + 8^2 = 25 + 144 + 64 = 233
b) The angle with the base is given by .