Shape and Space 9
3 marks · NormalA right triangular prism has end triangle sides 3 cm, 4 cm and 5 cm, and height (length perpendicular to end) of 10 cm.
Calculate the length of the longest diagonal from one vertex to the opposite vertex on the other end.
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
11.2 cm (±0.05)
Also accept: 11.18 cm
Common mistakes: Only using two sides.
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Recognises the diagonal as the hypotenuse across the prism: from one end vertex to the furthest opposite.
M2 · 1 mark · Uses Pythagoras: longest side squared plus height squared. (follow-through)
A1 · 1 mark · Correct value: 11.2 cm (3 sig fig). (follow-through)
Worked solution
The longest diagonal runs from the vertex at one triangle to the opposite vertex (on 5 cm side) at the other end. Use Pythagoras’ theorem: