Question

In a parallelogram PQRS of area 108 cm², the sides RS
and PS have lengths 9 cm and 16 cm respectively. Let
T be a point on RS such that PT I RS. Then, the area (in
sq. cm) of triangle PST is​

Answer 1

Given : In a parallelogram PQRS of area 108 cm², the sides RS

and PS have lengths 9 cm and 16 cm respectively. T is a point on RS such that PT ⊥ RS

To Find :  area (in  sq. cm) of triangle PST

Solution:

RS = 9 cm

PS = 16 cm

PT ⊥ RS

Area of Parallelogram = RS x PT  

=> 9 x PT  = 108

=> PT = 12 cm

    PS = 16 cm

ST² = PT² - PS²

=> ST² = 16² - 12²

=> ST² = 256  - 144

=> ST² = 112

=> ST  = 4√7

Area of ΔPST = (1/2) ST x PT

=  (1/2) 4√7  x  12

= 24√7

= 63.5  cm²

the area (in  sq. cm) of triangle PST =  63.5  

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