Questions on Prism

1.A prism with triangular base with sides AB=5cm, BC=8cm, and CA=7cm and Altitude (H)= 9cm. Find the Lateral surface Area, Total surface area, and Volume?
Ans: Since, triangle ABC is scalene triangle.
Perimeter (P) = 5+8+7 = 20cm
The area of ABC = √10*(10-5)*(10-8)*(10-7) = √(10*5*2*3) = 10√3.

LSA = Perimeter * Altitude = 20 * 9 = 108 cm2

TSA = LSA + 2 x Area of ABC = 108+20√3 cm2

Volume = Area x altitude = 10√3 * 9 = 90√3 cm3 

2. A pyramid with trapezium base with sides AB=9cm, BC=12cm, CD=15cm, and DA=18cm. The Volume of pyramid = 1458 cm3. Find the Height (H)?
Ans: 

3. A rectangle based pyramid, length and width of the base is 18 cm and 10 cm respectively. Find the total surface area (TSA), if its height is 12 cm?
Ans: 



4. A regular tetrahedron has surface area of 144√3. Find the side, volume and Total surface area (TSA)?
Ans: Lateral Surface area = 144√3 = √3 * side2
   => side2 = 144 => side = 12 cm.
   => TSA = 3√3/4 * side2 = 3√3/4 * 122 = 27√3 cm2.
   => Volume = √2/12 * side3 = √2/12 * 123 = 144V2