Answer :

**Given:** AP: PB = 1: 2

**To find:**

**Theorem Used:**

1.) If two corresponding angles of two triangles are equal, the triangles are said to be similar.

2.) The ratio of the areas of two similar triangles are equal to the ratio of the squares of any two corresponding sides.

**Explanation:**

We know PQ∥BC,

In ∆APQ and ∆ABC

∠A=∠A [Common]

∠APQ=∠B [Corresponding angle]

**∆ABC ~ ∆APQ**

From theorem 2.) stated above,

⇒ 9 ar(∆APQ) = ar(∆APQ) +ar (trapezium BPQC)

⇒ 9 ar(∆APQ)- ar(∆APQ) = ar(trapezium BPQC)

⇒ 8 ar(∆APQ) =ar (trapezium BPQC)

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