Solution,
Method 1
We know that the sum of the area of all rectangular surfaces is the lateral surface area of the prism. Hence using the formula for lateral surface area we get,
Lateral Surface Area = perimeter of base x height
Or, 480 cm2 = (AB+CA+BC) x AA'
Or, 480 cm2 = (10cm + 8cm +BC) x (20cm)
Or, 480 cm2 = (18 cm + BC ) x 20 cm
Or, 480 cm2 = 360 cm2 + 20xBC cm
Or, ( 480 - 360 ) cm2 = 20xBC cm
Or, 120cm2 = 20xBC cm
Or, \(BC=\frac{120cm^2}{20cm}\)
∴ BC = 6 cm
Method 2
In the given prism, the triangular face ABC is a right angles triangle. So, using Pythagoras theorem,
we have,
\(AB^2=BC^2+AC^2\)
Or, \(BC=\sqrt{AB^2-AC^2}\)
Or, \(BC=\sqrt{(10cm)^2-(8cm)^2}\)
Or, \(BC=\sqrt{36cm^2}\)
Or, \(BC=\sqrt{\left(6cm\right)^2}\)
∴ BC = 6 cm
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