Question

Find the area of $\Delta PCD$, P lies on the line AB, where O is the centre of the outer circle with radius 6.5 cm. ABCD is a rectangle, one of its sides is 5 cm.

• A. $30c{m}^2$
• B. $45c{m}^2$
• C. $36c{m}^2$
• D. $50c{m}^2$

Answer 1

The correct option is A $30c{m}^2$

If radius = 6.5 cm, then BD = 13 cm.
By Pythagoras theorem,
The other side of the rectangle has to be 12
(Since 5, 12 and 13 from a Pythagoras triplet)
So, area $\left(\Delta PCD\right)=\left(\frac{1}{2}\right)\times 12\times 5=30$
It does not matter which side is 12 or 5. Area remains the same.