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

Printable View

- Jan 11th 2011, 07:04 AMrn5aArea 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 - Jan 11th 2011, 07:14 AMAlso sprach Zarathustra
- Jan 11th 2011, 07:18 AMDrSteve
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?

- Jan 11th 2011, 07:51 AMrn5a
- Jan 11th 2011, 11:21 PMAlso sprach Zarathustra
$\displaystyle S$ 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 $\displaystyle \frac{a+b}{2}=\frac{64}{2}=32$

$\displaystyle S=m\cdot h=32\cdot 16=2^5 \cdot 2^4=2^9=512$ - Jan 12th 2011, 04:33 AMSoroban
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: .$\displaystyle \boxed{A \;=\;\tfrac{1}{2}h(b_1 + b_2)}$

. . 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 . . .