find the area of the trapezoid bounded by the graphs of the equations x=6,y=4,y=1/2x and the y axis?

Answer 1

Break it down to a square/rectangle and a right angled triangle. Its dead simple then.

Answer 2

When X = 6, solve for Y, Y = 1/2 ( 6) = 3

You will see a trapezium on the graph, take the height as 6 ( parallel to the x-axis, the lengths as 4 units and 1 units ( parallel to the y-axis )

1 unit comes from 4 - 3 = 1 ( This is the distance between the point where the line X = 6 cuts the line y = 1/2 x and the point where y = 4 cuts the line x = 6.)

Since you have a trapezium with the 2 parallel lengths of 4 and 1 unit and a height ( perpendicular distance, or shortest distance ) of 6 units between the 2 lengths, the area is

1/2 x ( 4 + 1 ) x 6 = 15 units sq.

For shapes with 2 parallel sides, add up the lengths of the 2 parallel sides and multiply by half the shortest distance between the 2 parallel sides.

Answer 3

The graph of x=6 and y=4 forms a rectangle with the y axis.

This area will be L x W = 24 cm^2 (or whatever units you like)

The graph of y = 1/2x and x=6 makes a large triangle. The area bounded by these two graphs and the X axis will be

A = 1/2 b*h, where b is the triangle's base, and h is the height.

A = 1/2 (6*3)

A = 9 cm^2 (or whatever units you are using, squared)

If you subtract this from the larger area, you will get 24 - 9 =

15 cm^2...

Regards,

Mysstere

Answer 4

A=h(b1=b2)/2=6(2+4)/2=3(6)=18

Answer 5

x = 6
y = 4
y = (1/2)x
x = 0

So the coordinates of the points are

(0,4), (0,0), (6,4), and (6,3)

(0,0) and (6,3)
D = sqrt((6 - 0)^2 + (3 - 0)^2)
D = sqrt(6^2 + 3^2)
D = sqrt(36 + 9)
D = sqrt(45)
D = 3sqrt(5)

Base Bottom = 4
Left Leg = 6
Top Base = 1
Right Leg = 3sqrt(5)

if you were to make the left side of the graph the main base, then all the rest will fall into place.

Area = h(a + c)/2

Height = 6, and just to make sure

h^2 = (a + b - c + d)(-a + b + c + d)(a - b - c + d)(a + b - c - d)/[4(a - c)^2].

(4 + 6 - 1 + 3sqrt(5))(-4 + 6 + 1 + 3sqrt(5))(4 - 6 - 1 + 3sqrt(5))(4 + 6 - 1 - 3sqrt(5))/(4(4 - 1)^2)

((9 + 3sqrt(5))(3 + 3sqrt(5))(-3 + 3sqrt(5))(9 - 3sqrt(5)))/(4(4 - 1)^2)

(-((9 + 3sqrt(5))(9 - 3sqrt(5)) * ((3 + 3sqrt(5))(3 - 3sqrt(5)))/(4(3)^2)

(-(81 - 27sqrt(5) + 3sqrt(5) - 45)(9 - 9sqrt(5) + 9sqrt(5) - 45)))/(4 * 9)

(-(81 - 45)(9 - 45))/(36)

(-(36)(-36))/(36)

(1296)/36

h^2 = 36
h = 6

so

A = h(a + c)/2
A = 6(4 + 1)/2
A = 3(5)
A = 15

ANS : 15 square units

Answer 6

that's not right
cuz
x=6
y=4
y=1/2*x
y=1/2*4
y=2 !

Answer 7

That'd take a whole HEAP o' cipherin'!

Answer 8

You give it a shot

Answer 9

i wont tell you the answer but your formula should be 1/2bh /\