Question

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal lengths. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then determine the total area, in sq cm, of all six surfaces of the pillar?

• A. 1340
• B. 1300
• C. 1550
• D. 1520
• E. 1480

Hint:

For a prism, the total surface area is $2 \times \text{Base Area} + \text{Perimeter of Base} \times \text{Height}$.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
A uniform pillar is a prism. Total surface area includes the top and bottom bases plus the lateral sides.
Step 2: Key Formula or Approach:
TSA \( = 2 \cdot \text{Base Area} + (\text{Base Perimeter} \cdot \text{Height}) \).
Step 3: Detailed Explanation:
1. Base Area \( = (1/2) \cdot (10 + 20) \cdot 12 = 180 \).
2. Side of trapezium (\( s \)):
Length difference \( = 20 - 10 = 10 \). For an isosceles trapezium, drop perpendiculars; split is \( 5, 10, 5 \).
\( s = \sqrt{12^2 + 5^2} = 13 \).
3. Base Perimeter \( = 10 + 20 + 13 + 13 = 56 \).
4. TSA \( = 2 \cdot (180) + (56 \cdot 20) = 360 + 1120 = 1480 \).
Step 4: Final Answer:
The total area is 1480 sq cm.