Try this beautiful problem from Geometry based on area of pinwheel.

## Pinwheel – AMC 8, 2007

What is the area of the shaded pinwheel shown in the \(5 \times 5\) grid?

- $8$
- $6$
- $9$

**Key Concepts**

Geometry

Triangle

Square

## Check the Answer

But try the problem first…

Answer:$6$

AMC-8 (2007) Problem 23

Pre College Mathematics

## Try with Hints

First hint

Find the area of white space

Can you now finish the problem ……….

Second Hint

The area of the pinwheel =Total area of the square – The white space

can you finish the problem……..

Final Step

Now The area of the square around the pinwheel is \(5 \times 5\)=25 sq.unit

Clearly in the above picture, there are four white triangles i.e (\(\triangle EOF, \triangle KOL, \triangle HOG, \triangle JOI)\) and four white small square(at the corner)

clearly HG=3 unit & OP=2.5 unit

Therefore the area of four Triangle = \(4 \times \frac{1}{2} \times HG \times OP= 4 \times \frac{1}{2} \times 3 \times\) 2.5=15 sq.unit

And also the area of four white corner squares =\((4 \times 1)\)=4 sq.unit

The area of the pinwheel =Total area of the square – The white space =(25-15-4)=6 sq.unit

## Other useful links

- https://www.cheenta.com/surface-area-of-a-cube-amc-8-2009-problem-25/
- https://www.youtube.com/watch?v=BXWGKh01nOw

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