The base of a right prism is an isosceles trapezium with parallel sides measuring 10 cm and 20 cm, and non-parallel sides measuring 13 cm each. The volume of the prism is 3240 cm3. What is the total surface area of the prism?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 1368 cm2.
Length of base projection = (20 – 10)/2 = 10/2 = 5 cm
Height (h) of trapezium = √(132 – 52) = √(169 – 25) = √144 = 12 cm
Area of trapezium = (1/2) × (10 + 20) × 12 = (1/2) × 30 × 12 = 180 cm2
Let the height of the prism = H cm
Volume of prism = Base area × Height of prism = 180 × H = 3240
⇒ H = 3240/180 = 18 cm
Lateral surface area = Perimeter of base × Height (H) = (10 + 20 + 13 + 13) × 18 = 56 × 18 = 1008 cm2
Total surface area = Lateral area + 2 × Base area = 1008 + 2 × 180 = 1368 cm2