ABCD is a trapezium in which ab is parallel to CD BC and area non parallel sides it is given that a b equal to 75 cm BC equal to 42 cm equal to 30 cm and area equals to 39 cm find the area of the trapezium
Answers
Answer:
Draw DE and CF perpendicular to AB.
Let AE = x and let BF = y, and DE = CF = h, and EF = CD = 30
Since AB = 75, x + 30 + y = 75
x + y = 45
By the Pythagorean theorem
x² + h² = 39²
y² + h² = 42²
x² + h² = 1521
y² + h² = 1764
Multiply the first equation by -1 and add the two equations:
-x² - h² = -1521
y² + h² = 1764
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y² - x² = 243
Factorise:
(y - x)(y + x) = 243, and since x + y = 45, y + x = 45
(y - x)(45) = 243
45(y - x) = 243
y - x = 243%2F45
y - x = 5.4
Add these two equations:
y + x = 45
y - x = 5.4
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2y = 50.4
y = 25.2
Substitute in:
y² + h² = 1764
(25.2)² + h² = 1764
635.04 + h² = 1764
h² = 1128.96
h = 33.6
Formula for area of trapezium
A = (base1 + base2)(height)/2
A = (75 + 30)(33.6)/2
A = 1764 cm²