PQRS is a square T U are respectively,the mid - points of PS QR find the area - Maths - Coordinate Geometry

Question

PQRS is a square T&U are respectively,the mid - points of
PS & QR find the area of triangle OTS,if PQ=8cm,where O is the
point of intersection of TU & QS
ABCD is a parallelogram in which BC is produced to E suh that
CE=BC AE intersects CD at F if ar(DFB)=3cm2find the area
of the parallelogram ABCD

Gursheen kaur. · Accepted Answer

1) Given : PQRS is a square with T and U as mid points of side PS and QR respectively and QS and TU intersect at point O Since T and U are mid points of PS and QR respectively âˆ´ TU || PQ â‡’ TO || PQ Thus in Î”PQS, T is the mid point of PS and TO || PQ $\Rightarrow TO = \frac{1}{2} PQ = \frac{1}{2} \times 8 = 4 cm Also, TS = \frac{1}{2} PS = \frac{1}{2} \times 8 = 4 cm ∴ ar (Δ DTS) = \frac{1}{2} (TO \times TS) = \frac{1}{2} \times 4 \times 4 {cm}^{2} = 8 {cm}^{2}$

2) $G i v e n : a r e a (D F B) = 3 {c m}^{2} a r e a (∥ g m A B C D) = 2 (a r e a Δ A D B) w h e r e a r e a (D F B) = (a r e a Δ A D B) [∵ T h e y l i e b e t w e e n s a m e b a s e B D & b e t w e e n s a m e p a r a l l e l l i n e s A B & D F] \Rightarrow a r e a (∥ g m A B C D) = 2 \times 3 \Rightarrow a r e a (∥ g m A B C D) = 6 {c m}^{2}$