A rectangular parallelepiped has its base diagonal equal to 17 cm and height 15 cm. If the area of its base is 120 cm², find the total surface area of the parallelepiped.
Show answer & explanation
Correct answer: B
Explanation
Given:
Diagonal of base = 17 cm
Height = 15 cm
Area of base = 120 cm²
By formula:
Total surface area = 2(lb + bh + lh)
Let the sides of the base = l and b
lb = 120
Diagonal
l² + b² = 17²
= 289
(l + b)² = l² + b² + 2lb
= 289 + 240
= 529
l + b = 23
lb + bh + lh = 120 + 15(l + b)
= 120 + 15 × 23
= 120 + 345
= 465
Total surface area = 2 × 465 = 930 cm²