2009 WAEC Mathematics Theory In the diagram, ABCDEF is a triangular prism. &lt; ABC = &lt; DEF = 90&deg;,...

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.

(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)

= \(( 2 \times 84 cm^{2}) + (25 \times 40)cm^{2} + (24 \times 40)cm^{2} + (7 \times 40)cm^{2}\)

= \((168 + 1000 + 960 + 280) cm^{2}\)

= \(2408 cm^{2}\)

{{ settings.no_comment_msg ? settings.no_comment_msg : 'There are no comments' }}