# Find the area of the quadrilateral

• chwala
In summary, the conversation discusses the possibility of finding the area of a quadrilateral with given dimensions. It is determined that the area cannot be found due to incomplete information. The use of sine, cosine rule, and the angle property of parallelogram are mentioned, but it is concluded that basic geometry is sufficient. The conversation ends with an acknowledgement that the area cannot be determined.
chwala
Gold Member
Homework Statement
See attached
Relevant Equations
sine rule
I was looking at this problem today, and i was trying to figure out its area with the given dimensions shown. First, is this even possible?...i later looked at the problem in detail and realized that i had missed out on some dimension that was given on the text.
Having said that, i would like to try and see if its possible to find the area of the quadrilateral with the given dimensions as indicated...i would nevertheless like to know whether this is possible. I will try look at it and share my working later...i will make use of sine, cosine rule and the angle property of parallelogram...

Last edited:
There is not enough to determine where point ##D## is. The area of triangle ##ACD## could be anything.

PeroK said:
There is not enough to determine where point ##D## is. The area of triangle ##ACD## could be anything.
I was thinking of angle ##B##+##D##=##180^0##... this has to fix the point ##D## at some point...

chwala said:
I was thinking of angle ##B##+##D##=##180^0##... this has to fix the point ##D## at some point...
You can put D wherever you like. BCD is any triangle with a base of 5m.

sysprog
chwala said:
I was thinking of angle ##B##+##D##=##180^0##... this has to fix the point ##D## at some point...
Angles B and D would only add to 180 degrees for a cyclic quadrilateral.

Let me try and crack this tomorrow...sorry i have been a bit busy with work...let's see where i reach on this...i will try and find the dimensions of the quadrilateral...of course by use of the parallelogram property...then i may agree with you if its impossible...thanks Perok and Steve4Physics man!

Steve4Physics said:
Angles B and D would only add to 180 degrees for a cyclic quadrilateral.
Aaargh that's true...i overlooked that! let's see how far I go with this...

@chwala, what part of @PeroK's point escaped you? You don't need trig functions and such for this; it's 5th grade geometry:

##\mathrm{area~of}~\triangle = \frac 12(\mathrm{base}\times\mathrm{height})##.

In the illustration, increasing the lengths of CD and AD would increase the height. Since we don't know those lengths, we can't find the area of triangle ACD, and without knowing that area, we can't know the area of quadrilateral ABCD.

PeroK and chwala
sysprog said:
@chwala, what part of @PeroK's point escaped you? You don't need trig functions and such for this; it's 5th grade geometry:

##\mathrm{area~of}~\triangle = \frac 12(\mathrm{base}\times\mathrm{height})##.

In the illustration, increasing the lengths of CD and AD would increase the height. Since we don't know those lengths, we can't find the area of triangle ACD, and without knowing that area, we can't know the area of quadrilateral ABCD.
True, it's not possible to find the area...I just tried looking at it...cheers mate...

sysprog

## 1. What is a quadrilateral?

A quadrilateral is a geometric shape with four sides and four angles.

## 2. What are the different types of quadrilaterals?

The different types of quadrilaterals include squares, rectangles, parallelograms, rhombuses, trapezoids, and kites.

## 3. How do you find the area of a quadrilateral?

The formula for finding the area of a quadrilateral depends on the type of quadrilateral. For example, the area of a square or rectangle is found by multiplying the length by the width. The area of a parallelogram is found by multiplying the base by the height. The area of a rhombus is found by multiplying the two diagonals and dividing by 2. The area of a trapezoid is found by multiplying the average of the two bases by the height.

## 4. Can you find the area of a quadrilateral if you only know the length of the sides?

Yes, you can use the Heron's formula to find the area of a quadrilateral if you know the length of all four sides. This formula is: area = √(s(s-a)(s-b)(s-c)(s-d)), where s is the semi-perimeter (half of the perimeter) and a, b, c, and d are the lengths of the sides.

## 5. What units are used to measure the area of a quadrilateral?

The area of a quadrilateral is typically measured in square units, such as square inches, square feet, or square meters.

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