Sum

Look at the measures shown in the adjacent figure and find the area of ☐ PQRS.

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#### Solution

Join PR.

In triangle PSR,

Applying Pthygoras theorem,

PS² + SR² = PR²

⇒ 36² + 15² = PR²

⇒ PR² = 1296 + 225 = 1521

⇒ PR = `sqrt[1521]` = 39 m

In triangle PQR,

s = `(56 + 25 + 39)/2 = 60`

Area =`sqrt[60 ( 60 - 56) (60 -25) (60 -39)]`

= `sqrt[60 xx 4 xx 35 xx 21]`

= `sqrt[176400]`

= 420 m²

Area of triangle PSR = `1/2 xx 15 xx 36` = 270 m²

Area of PQRS = Area of triangle PSR + Area of triangle PQR

= 270 + 420

= 690 m^{2}

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