Question 14 of 14intermediate🔧 ApplyLong Answer4 marks

Using the idea of converting a trapezium into a rectangle of equal area, and vice versa, construct a trapezium of area 144 cm².

Correct Answer

Step 1: Choose dimensions for area 144 cm², e.g., rectangle 16 cm × 9 cm.

Step 2: Rectangle length 16 cm = average of trapezium's parallel sides.

Step 3: Choose parallel sides such that (a + b)/2 = 16, e.g., a = 12, b = 20.

Step 4: Height = 9 cm.

Step 5: Verify: Area = ½ × 9 × (12 + 20) = ½ × 9×329 \times 32 = 144 cm²

Why it works: A trapezium with parallel sides a and b, and height h has the same area as a rectangle with length (a+b)/2 and width h.

Exercise: Figure it Out (Section 5) | Q: 6 | (Page Page 23)
For More Understanding

Explanation

The chapter establishes the relationship between trapezium and rectangle areas. A trapezium with parallel sides a and b, and height h has the same area as a rectangle with length (a+b)/2 and width h.

Solution Steps

  1. Step 1: Choose dimensions for area 144 cm², e.g., rectangle 16 cm × 9 cm.

  2. Step 2: Rectangle length 16 cm = average of trapezium's parallel sides.

  3. Step 3: Choose parallel sides such that (a + b)/2 = 16, e.g., a = 12, b = 20.

  4. Step 4: Height = 9 cm.

  5. Step 5: Verify: Area = ½ × 9 × (12 + 20) = ½ × 9×329 \times 32 = 144 cm².

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