In the adjoining figure ABCD is a trapezium into which parallel sides are AB=78 cm,DC=52cm,and the non parallel sides are BC=30 cm,and AD=28 cm.find the area of trapezium?
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Area of figure ABCD = 1680 cm² if in ABCD parallel sides are AB=78 cm, DC=52cm, and the non parallel sides are BC=30 cm, AD=28 cm
Step-by-step explanation:
AB = 78 cm
CD = 52 cm
BC = 30 cm
AD = 28 cm
Draw DM & CN ⊥ AB
DM = CN = P
MN = CD = 52 cm
AM = x cm
BN = 78 - 52 - x = 26 - x cm
28² - P² = x²
30² - P² = (26 - x)²
=> 30² - 28² = (26 - x)² - x²
=> 58 * 2 = 26 * (26 - 2x)
=> 29 = 13 (13 - x)
=> 13 -x = 29/13
=> x = 140/13
28² - P² = x²
=> P² = 28² - (140/13)²
=> P² = (504) 224 / 13²
=> P = 336/13 cm
Area of figure ABCD = (1/2) ( 78 + 52) * 336/13
= (6 + 4) 168
= 1680 cm²
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