Please help
Polygon ABCD has the following vertices:
A(−5, 4), B(1, 4), C(6, −4), and D(−5, −4)
Calculate the area of the polygon.
48 units
53 units
68 units
88 units

- anonymous

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- anonymous

|dw:1433643772301:dw|
Well... Here is a graphical image of what we are dealing with

- anonymous

ok

- anonymous

So we have to calculate the area of this shape.
This shape is a trapezium
So you know the area formula for the trapezium?

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## More answers

- anonymous

nope

- anonymous

it is:
A = 1/2 (h) ( a + b )

- anonymous

Okay so, we have to break this formula down bit by bit, to get the correct values to substitute into the equation :)

- anonymous

ok

- anonymous

firstly, let's solve for 'h'

- anonymous

Okay, now the 'h' is determined by the points A and D
How high, in terms of units, do you think it is?

- anonymous

18

- anonymous

or do I multiply

- anonymous

I'll draw another diagram to see what we are working with okay :)

- anonymous

ok

- anonymous

|dw:1433644144157:dw|

- anonymous

So how many units apart are the y values? in order to find the value for h ~

- anonymous

IN this case you add, to calculate the distance

- anonymous

27?

- anonymous

It is actually 8, can you tell me why?

- anonymous

I have no idea

- anonymous

okay see how the points A (-5,4) and D (-5,-4) ?

- anonymous

yup

- anonymous

These points represent dots on a diagram
With this information we can tell their distances apart
in this case we are looking for 'h', so we are looking at the y values in A and D

- anonymous

how do we tell them apart?

- anonymous

The 'y' values in points A and D are see in the second number of the point
For example
A (-5,4)
4 = 4 units upwards
Whereas:
D = (-5,-4)
-4 = -4 units downwards

- anonymous

ohh ok

- anonymous

So the calculation for h is
4 + 4 = 8

- anonymous

That's just for 'h' XD
now we have to find 'a' and 'b' ^^

- anonymous

so between A and D is 8 right?

- anonymous

yes that's right

- anonymous

can I solve A and B for practice?

- anonymous

We can work out the rest of 'a' and 'b' and if there is anything in the end, that you don't understand, I'll gladly go through it again :)

- anonymous

yeah sure, i'll check if your correct or not for A and B ^^

- anonymous

is it 8 again?

- anonymous

wait nvm

- anonymous

For the value of 'a' which is from point A to B
It is actually 6 units

- anonymous

|dw:1433644991291:dw|

- anonymous

So we are calculating for the 'a' in the formula. We have to look at the x values in the points
For example:
A(-5,4)
-5 = 5 units to the left hand side
B(1,4)
1 = 1 units to the right hand side

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