1. ## Area Of Trapezium

The perimeter of a trapezium is 104 m; its non-parallel sides are 18 m & 22 m & its altitude is 16 m. How do I find the area of the trapezium?

Thanks,

Ron

2. Originally Posted by rn5a
The perimeter of a trapezium is 104 m; its non-parallel sides are 18 m & 22 m & its altitude is 16 m. How do I find the area of the trapezium?

Thanks,

Ron
I don't really know if it will help.

Find the mid-segment and multiply him by the height(16m).

3. The Area is the height times the average of the bases. The sum of the bases is 104-18-22. Can you take it from here?

4. Originally Posted by DrSteve
The Area is the height times the average of the bases. The sum of the bases is 104-18-22. Can you take it from here?
I tried what you suggested but can't proceed ahead. How do I get the average of the bases from the sum of the bases? Can you please help me out? Thanks

OK.....I got it.........thanks a lot.......

5. Originally Posted by rn5a
I tried what you suggested but can't proceed ahead. How do I get the average of the bases from the sum of the bases? Can you please help me out? Thanks

OK.....I got it.........thanks a lot.......
$\displaystyle S$ is the area.

We have this formula for an area of trapezium:

$\displaystyle S=m\cdot h$

Where $\displaystyle h$ is the height and $\displaystyle m$ is mid-segment of trapezium, or:

$\displaystyle m=\frac{a+b}{2}$

Lets find first $\displaystyle a+b$.

$\displaystyle a+b=104-18-22=64$

Therefor $\displaystyle \frac{a+b}{2}=\frac{64}{2}=32$

$\displaystyle S=m\cdot h=32\cdot 16=2^5 \cdot 2^4=2^9=512$

6. Hello, Ron!

The perimeter of a trapezium is 104 m.
Its non-parallel sides are 18 m & 22 m.
Its altitude is 16 m.
How do I find the area of the trapezium?
Use the area formula.

Formula: .$\displaystyle \boxed{A \;=\;\tfrac{1}{2}h(b_1 + b_2)}$

. . where .$\displaystyle \,h$ = height, $\displaystyle b_1,b_2$ = parallel sides.

Code:

b1
*  *  *  *  *
*              *
18 *                 *  22
*                    *
*                       *
*                          *
*  *  *  *  *  *  *  *  *  *  *
b2

The perimeter is 104 m.

. . $\displaystyle b_1 + 22 + b_2 + 18 \:=\:104 \quad\Rightarrow\quad \boxed{b_1 + b_2 = 64}$

We are given: .$\displaystyle \boxed{h \,=\,16}$

Substitute into the formula . . .

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# the paremeter of a trapezium is 104m its non parallel sides are 18 m and 22 m and its altitude is 16 m find the area

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