A prism-shaped chocolate box has an equilateral triangular base of side 12 cm and a height of 25 cm. If 25 such boxes are packed in a crate, what is the total surface area of all the boxes, including their tops and bottoms? (Use √3 = 1.732)
Show answer & explanation
Correct answer: B
Explanation
Given:
Side of the equilateral triangle = 12 cm
Height of the prism = 25 cm
Number of boxes = 25
According to the formula:
Area of an equilateral triangle = (√3 / 4) × a²
Total Surface Area = Lateral Surface Area + 2 × Base Area
Lateral Surface Area = Perimeter of the base × Height
Perimeter of the base = 3 × 12 = 36 cm
Lateral Surface Area = 36 × 25 = 900 cm²
Base Area = (√3 / 4) × 12² = 62.352 cm²
Total Surface Area (for one box) = 900 + 2 × 62.352 = 1024.704 cm²
Total Surface Area for 25 boxes = 1024.704 × 25 = 25617.6 cm²