Question

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

Answer 1

In triangle PSR,

Applying Pythagoras theorem,

PS²  + SR²  = PR² 

⇒ 36²  + 15²  = PR² 

⇒ PR²  = 1296 + 225

⇒ PR² = 1521

⇒ PR = `sqrt[1521]`

⇒ PR = 39 m

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

In triangle PQR,

by using Heron's formula,

Let a = 56, b = 25, c = 39

So,

s = `(a + b + c)/2`

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

s = 60

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

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

= `sqrt[176400]`

= 420 m²

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

= 270 + 420

= 690 m²