Question

in triangle abc,pq is parallel to ab .if cp/pa= 3/1 and area of triangle anc=64cm^2 .find the area 0f the quadrilateral abqp​

Answer 1

Answer:

Area of quadrilateral ABQP=28cm^2

Step-by-step explanation:

∆ABC is similar to ∆PCQ

A(∆PCQ)/A(∆ABC) = PQ^2/AB^2 => QC^2/BC^2 => CP^2/AC^2

CP/AP = 3/1 => AP/CP => 1/3 => AP/CP + 1 = 1/3 + 1

=> (AP + CP)/CP = 4/3 => AC/CP = 4/3

=> CP/AC = 3/4

=> CP^2/AC^2 = 9/16

Therefore, Area of ∆PCQ = 9/16 × 64 = 36cm

Area of quadrilateral APQB = A(∆QBC) - A(∆PQC) => 64-36

Therefore, area of quadrilateral APQB = 28cm^2

Something tells me that you would've already gotten the answer to this question, - why, perhaps even today - but I'm answering this for the going-to-be poor souls who'd have to sit through a tution. You're welcome.