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)
= \(( 2 \times 84 cm^{2}) + (25 \times 40)cm^{2} + (24 \times 40)cm^{2} + (7 \times 40)cm^{2}\)
= \((168 + 1000 + 960 + 280) cm^{2}\)
= \(2408 cm^{2}\)