PQRS is a parallelogram A, B, C and D are the mid points of sides PQ, QR, RS and - Maths - Areas of Parallelograms and Triangles

Question

PQRS is a parallelogram A, B, C and D are the mid points of
sides PQ, QR, RS and PS respectively If area of triangle DAC is
equal to 10cm2 Find the area of triangle ABC

Manbar Singh · Accepted Answer

We have PQRS as the parallelogram, in which A, B, C and D are the
mid points of the sides PQ, QR, RS and SP
Join PR and AC
Since A and B are the mid points of the sides PQ and QR in
âˆ† PQR, so,
AB ∥ PR and AB = 12 PR    mid point theorem  
1

Since D and C are the mid points of the sides SP and SR in △ SPR, thenDC ∥ PR   and DC = 12PR    mid point theorem    
2From 1 and 2, we getAB ∥ DC  and AB = DCIn quad
 ABCD , we haveAB ∥ DC  and AB = DC⇒quad
 ABCD  is a parallelogram Since in a quadrilateral, if a pair of opposite sides is equal and parallel, then quadrilateral is a ||gm
Since AC is the diagonal of ||gm ABCD , so,ar△ADC = ar△ABC diagonals of ||gm divides it into 2 △'s of equal areas⇒ar△ABC = 10 cm2    , as ar△ADC = 10 cm2

PQRS is a parallelogram. A, B, C and D are the mid points of sides PQ, QR, RS and PS respectively. If area of triangle DAC is equal to 10cm2. Find the area of triangle ABC.

PQRS is a parallelogram. A, B, C and D are the mid points of sides PQ, QR, RS and PS respectively. If area of triangle DAC is equal to 10cm^2.Find the area of triangle ABC.