In 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.
Explanation
(a) From the diagram,
(|AC|^{2} = 24^{2} + 7^{2})
= (576 + 49)
(|AC|^{2} = 625 implies |AC| = sqrt{625} = 25 cm)
(Area = frac{1}{2} times b times h)
= (frac{7 times 24}{2})
= (84 cm^{2}).
(b) Total Surface Area of prism
= Area of two right angles ( ABC and EFD) + Area of 3 rectangles (ACDF, ABEF and BCDE)
= (( 2 times 84 cm^{2}) + (25 times 40)cm^{2} + (24 times 40)cm^{2} + (7 times 40)cm^{2})
= ((168 + 1000 + 960 + 280) cm^{2})
= (2408 cm^{2})