# trignometry

• Sep 7th 2008, 03:01 AM
dolly kohli
trignometry
Hi! can you solve this sum for me---
PQRS is a quadrilateral.The sides RS and QR are the same length.The sides QP and RS are parallel.Calculate:
1)angle SQR
2)angle PSQ
3)length PQ
4)length PS
5)Area of PQRS
• Sep 7th 2008, 01:11 PM
Soroban
Hello, dolly kohli!

Obviously, some information is missing . . .

Quote:

can you solve this sum for me --- sum?

Sides RS and QR are the same length.
Sides QP and RS are parallel.

Calculate:

$\displaystyle 1)\;\angle SQR\qquad 2)\;\angle PSQ\qquad 3)\;\text{ length }PQ \qquad 4)\;\text{ length }PS \qquad 5)\;\text{ Area of }PQRS$

Code:

P                            Q
o  *  *  *  *  *  *  *  *  *  o
θ  * *
* θ *
*              *    *
*        *      *
*    * θ      *
o  *  *  *  o
S          R

Since $\displaystyle RS = QR,\;\Delta QRS$ is isosceles.
. . Hence: .$\displaystyle \angle SQR \:=\:\angle QSR \:=\:\theta$

Since $\displaystyle QP \parallel RS,\;\angle PQS \:=\:\angle QSR \:=\:\theta$

Since $\displaystyle P$ can be anywhere to the upper-left on that line,
. . we cannot determine $\displaystyle \angle PSQ$

Nor can we find the lengths of $\displaystyle PQ$ and $\displaystyle PS$, or the area of $\displaystyle PQRS$.