Determine graphically the vertices of a trapezium, the equations of
whose sides are x = 0,
y = 0, y = 4 and 2x + y = 6. Also determine its area.
Answers
Given : the equations of trapezium sides are x = 0, y = 0, y = 4 and 2x + y = 6
To find : Determine graphically the vertices of a trapezium
Solution:
x = 0
y = 0
y = 4
2x + y = 6
y = 0 & y = 4 are parallel lines
y = 0 & y = 4 with x = 0
will form two points
(0 , 0) & ( 0 , 4)
y = 0 & y = 4 with 2x + y = 6
will form points
(3 , 0) & ( 1 , 4)
See attached figure of trapezium
Parallel side length
= √(1 - 0) ² + (4 - 4)² = 1
& √(3 - 0) ² + (0 - 0)² = 3
Height = 4
Area of trapezium = (1/2)( 1 + 3) * 4
= 8
Area of trapezium = 8 sq units
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The area of the trapezium is 8 sq.units.
Step-by-step explanation:
The equation 2x + y = 6 is:
x | 0 | 3
y | 6 | 0
The area between the equations is given by the points A(0, 0), B(3, 0), C(2, 4) and D(0, 4).
The area of trapezium is given as:
A = 1/2 × (Sum of the sides) × (Distance between them)
A = 1/2 × (CD + AB) × DA
On substituting the values, we get,
A = 1/2 × (1 + 3) × 4
A = 1/2 × 4 × 4
A = 1/2 × 16
∴ A = 8 sq.units