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 parallel to RS. Then, the area (in
sq. cm) of traingle PST is
Answers
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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