Question 7 of 14intermediate🔧 ApplyLong Answer3 marks

[Śulba-Sūtras] Give a method to obtain a rectangle of the same area as a given triangle.

Correct Answer

Given: A triangle with base b and height h.

Step 1: Triangle area = ½ × b × h

Step 2: Construct a rectangle with base = b.

Step 3: Make the rectangle height = h/2.

Step 4: Rectangle area = b × (h/2) = ½ × b × h ∴ Rectangle area = Triangle area

Alternative Method (by dissection): Cut the triangle at mid-height and rearrange the two pieces to form a rectangle.

Exercise: Figure it Out (Section 4) | Q: 6 | (Page Page 17)
For More Understanding

Explanation

The chapter discusses Śulba-Sūtras methods for transforming shapes while preserving area. The key insight is that a triangle's area equals a rectangle with the same base but half the height.

Solution Steps

  1. Step 1: Triangle area = ½ × b × h.

  2. Step 2: Construct rectangle with base = b.

  3. Step 3: Make rectangle height = h/2.

  4. Step 4: Rectangle area = b × h/2 = ½ × b × h = Triangle area.

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