Question
Download Solution PDFThe parallel sides of a trapezium are 48 cm and 20 cm. Its non-parallel sides are 26 cm and 30 cm. What is the area (in cm²) of the trapezium ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Parallel sides: a = 48 cm, b = 20 cm
Non-parallel sides: c = 26 cm, d = 30 cm
Formula used:
Area of trapezium = ½ × (a + b) × height (h)
Height (h) found using: h = √(c² - m²), where m = ((a - b)² + c² - d²) / (2 × (a - b))
Calculations:
a - b = 48 - 20 = 28
m = [28² + 26² - 30²] / (2 × 28)
m = (784 + 676 - 900) / 56 = (560) / 56 = 10
h = √(26² - 10²) = √(676 - 100) = √576 = 24 cm
Area = ½ × (48 + 20) × 24 = ½ × 68 × 24 = 34 × 24 = 816 cm²
∴ Area of the trapezium = 816 cm².
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