 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

But try the problem first…

Answer:$6$

Source

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