NTSE Stage 2 SAT 2015 Question Paper

Question : 50 of 100

Marks: +1, -0

In the figure, PQSO is a trapezium in which PQ||OS, POS 135 and OQS 90 . Points P, Q and R lie an a circle with centre O and radius 12cm. The area of the shaded part, in

\cm^2

, is

$61 2/7$
$61 5/7$
$73 5/7$
$73 2/7$

Validate

Solution:

As PQ||QS
⇒

∠\POS+\MOP=180°

⇒

35°∠\P=180°

∴

∠\P=45°

Now Radius

=12\cm

∴

√2 \x=12

∴

\x=6√2 \cm

∴ Area of shaded portion

=135°/360×π(12)^2-\text "Area of trapezium"

=135°/360×\π×144-1/2×(2\x+\x)×\x

=135°/360×22/7×144-1/2×3\x^2

=135°/360°×22/7×144-1/2×3×72

=1188/7-108=432/7=61 5/7

∴ Option (b) is correct.

Go to Question:

Prev Question

Next Question