Theory question 105
Mensuration of SolidsIn the diagram, ABCDEF is a triangular prism. ∠ABC = ∠DEF = 90°, |AB| = 24 cm, |BC| = 7 cm and |CD| = 40 cm. Calculate: (a) |AC|; (b) the total surface area of the prism.
Show the model answer
Model answer
(a) |AC| = √(242 + 72) = √625 = 25 cm.
(b) Two triangular ends: 2 × ½ × 24 × 7 = 168 cm2.
Three rectangles: 40 × (24 + 7 + 25) = 40 × 56 = 2240 cm2.
Total surface area = 2408 cm2.
Explanation
The rectangular faces together equal the perimeter of the triangle times the length.