# Math Help - Area of triangle

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

-------------------------------------------
(a)
triangle PQT = $\frac {\sqrt 3}{ 4 }xy$
(b)
triangle QRT = $\frac{\sqrt 3}{4}(20-x)y
$

(c)
don't know how to do (c)

Thanks in advance!

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

-------------------------------------------
(a)
triangle PQT = $\frac {\sqrt 3}{ 4 }xy$
(b)
triangle QRT = $\frac{\sqrt 3}{4}(20-x)y
$

(c)
don't know how to do (c)

Thanks in advance!
You've clearly made a couple of typos in the 'given', but judging by the answers to (a) and (b), I assume you mean
$PT = x$ and $QT = y$
and you've then used the $\tfrac12ab\sin C$ formula for the area of a triangle, where $\sin 60^o =\frac{\sqrt3}{2}$.

For (c), use the same method again to find the areas of $\triangle$ s $PTS$ and $STR$ (where $TS = 15-y$), and then add all four areas together.

Can you complete it now?

Grandad