please solve with Process and Soon
Answers
Answer:
x is equal to 60 and Y is equal to 40
Answer:
Answer:
The area of the trapezium is 1644 m².
Step-by-step-explanation:
NOTE: Refer to the attachment for the diagram.
In figure, □ABCD is a trapezium.
AB ∥ CD
AB = 60 m
CD = 77 m
AD = 25 m
BC = 26 m
Now,
Draw BP ∥ AD and BQ ⊥ PC.
∴ □ABPD is a parallelogram.
∴ AB = PD = 60 m
AD = BP = 25 m
Now,
CD = PD + PC - - - [ C - P - D ]
⇒ PC = CD - PD
⇒ PC = 77 - 60
⇒ PC = 17 m
Now, in △BPC,
BP ( a ) = 25 m
PC ( b ) = 17 m
BC ( c ) = 26 m
Semi perimeter = ( Sum of sides ) / 2
⇒ s = ( a + b + c ) / 2
⇒ s = ( 25 + 17 + 26 ) / 2
⇒ s = ( 25 + 25 + 17 + 1 ) / 2
⇒ s = ( 50 + 18 ) / 2
⇒ s = 68 ÷ 2
⇒ s = 34 m
Now, by Heron's formula,
Area of triangle = √[ s ( s - a ) ( s - b ) ( s - c ) ]
⇒ A ( △BPC ) = √[ 34 ( 34 - 25 ) ( 34 - 17 ) ( 34 - 26 ) ]
⇒ A ( △BPC ) = √( 34 * 9 * 17 * 8 )
⇒ A ( △BPC ) = √( 17 * 2 * 9 * 17 * 8 )
⇒ A ( △BPC ) = √( 17 * 17 * 3 * 3 * 16 )
⇒ A ( △BPC ) = √( 17 * 17 * 3 * 3 * 4 * 4 )
⇒ A ( △BPC ) = 17 * 3 * 4
⇒ A ( △BPC ) = 204 m²
Also,
Area of triangle = ( Base * Height ) / 2
⇒ A ( △BPC ) = ( PC * BQ ) / 2
⇒ 204 = ( 17 * BQ ) / 2
⇒ 17 * BQ = 204 * 2
⇒ BQ = ( 204 * 2 ) / 17
⇒ BQ = 204 ÷ 17 * 2
⇒ BQ = 12 * 2
⇒ BQ = 24 m
Now, we know that,
Area of trapezium = ( Sum of parallel sides * Height ) / 2
⇒ A ( □ABCD ) = [ ( AB + CD ) * BQ ] / 2
⇒ A ( □ABCD ) = [ ( 60 + 77 ) * 24 ] / 2
⇒ A ( □ABCD ) = ( 60 + 77 ) * 24 ÷ 2
⇒ A ( □ABCD ) = ( 60 + 77 ) * 12
⇒ A ( □ABCD ) = 12 * 60 + 12 * 77
⇒ A ( □ABCD ) = 720 + 12 * ( 70 + 7 )
⇒ A ( □ABCD ) = 720 + 840 + 84
⇒ A ( □ABCD ) = 1560 + 84
⇒ A ( □ABCD ) = 1644
∴ Area of trapezium = 1644 m²
∴ The area of the trapezium is 1644 m².