in a Trapezium ABCD ab parallel DC a b equal to 30 cm BC equal to 15 cm is equal to 40% and equal to 13 cm find the area of a Trapezium
Answers
Area of Trapezium = 444 cm²
Step-by-step explanation:
AB = 30 cm BC = 15 cm CD = 44 cm AD = 13 cm
Let draw AM ⊥ CD & BN⊥ CD
=> MN = AB = 30 cm
Let Say DM = a & CN = b
then DM + MN + CN = 44
=> a + 30 + b = 44
=> a + b = 14
now AM = BN ( perpendicular distance between parallel lines)
AM² = AD² - DM²
BN² = BC - CN²
=>AD² - DM² = BC² - CN²
=> 13² - a² = 15² - b²
=> b² - a² = 15² - 13²
=> (b + a)(b - a) = (28)(2)
=> 14(b - a) = 56
=> b - a = 4
a + b = 14
adding both
=> 2b = 18
=> b = 9
a = 5
AM² = AD² - DM²
=> AM² = 13² - 5²
=> AM² = 144
=> AM = 12
Area of Trapezium = (1/2) (AB + CD) * AM
= (1/2)(30 + 44)12
= 444 cm²
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