1. ## Area of triangle

Given PR = 20 , QS = 15 , PR = x , QS = y , angle PTQ = 60 degree

(a)
Find the area of triangle PQT

(b)
Find the area of triangle QRT

(c)
Using (a) and (b), find the area of PQRS

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(a)
triangle PQT =$\displaystyle \frac {\sqrt 3}{ 4 }xy$
(b)
triangle QRT = $\displaystyle \frac{\sqrt 3}{4}(20-x)y$
(c)
don't know how to do (c)

2. Hello cakeboby
Originally Posted by cakeboby

Given PR = 20 , QS = 15 , PR = x , QS = y , angle PTQ = 60 degree

(a)
Find the area of triangle PQT

(b)
Find the area of triangle QRT

(c)
Using (a) and (b), find the area of PQRS

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(a)
triangle PQT =$\displaystyle \frac {\sqrt 3}{ 4 }xy$
(b)
triangle QRT = $\displaystyle \frac{\sqrt 3}{4}(20-x)y$
(c)
don't know how to do (c)

$\displaystyle PT = x$ and $\displaystyle QT = y$
and you've then used the $\displaystyle \tfrac12ab\sin C$ formula for the area of a triangle, where $\displaystyle \sin 60^o =\frac{\sqrt3}{2}$.
For (c), use the same method again to find the areas of $\displaystyle \triangle$ s $\displaystyle PTS$ and $\displaystyle STR$ (where $\displaystyle TS = 15-y$), and then add all four areas together.