# Area of triangle

#### 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)

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Hello cakeboby
View attachment 16981
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 =$$\displaystyle \frac {\sqrt 3}{ 4 }xy$$
(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.