# Area Of Trapezium

• January 11th 2011, 08:04 AM
rn5a
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
• January 11th 2011, 08:14 AM
Also sprach Zarathustra
Quote:

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).
• January 11th 2011, 08:18 AM
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?
• January 11th 2011, 08:51 AM
rn5a
Quote:

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.......
• January 12th 2011, 12:21 AM
Also sprach Zarathustra
Quote:

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.......

$S$ is the area.

We have this formula for an area of trapezium:

$S=m\cdot h$

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

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

Lets find first $a+b$.

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

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

$S=m\cdot h=32\cdot 16=2^5 \cdot 2^4=2^9=512$
• January 12th 2011, 05:33 AM
Soroban
Hello, Ron!

Quote:

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

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

Code:

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

The perimeter is 104 m.

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

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

Substitute into the formula . . .