Question

the base of right prism is quadrilateral ABCD AB=9cm BC=14cm CD=13cm DA=12cm angle DAB=90 volume of prism be 2070 then area of lateral surface area is........

Answer 1

   BD² = BA² + AD² = 9² + 12² = 225 cm²
         BD = 15 cm

       Area of ABD = 1/2 * AB *AD = 54 cm²

   In triangle BCD,  s = (14+13+15)/2 = 21 cm

      Area of triangle BCD = √[ 21(s-a)(s-b)(s-c) ]  = √[21* 7*8*6] = 84 cm²

  =>  Total base area = 138 cm²

  Height = volume/base area = 2,070/138 = 15 cm
 
    Lateral surface area of the right prism = height * perimeter of the base = 
                      = 15 * (9+14+13+12) = 720 cm²