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Area of pinwheel | AMC 8, 2007 | Problem 23

Try this beautiful problem from AMC 8, 2007 Geometry based on pinwheel.You may use sequential hints to solve the problem

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

Answer:$6$

AMC-8 (2007) Problem 23

Pre College Mathematics

Try with Hints

Find the area of white space

Can you now finish the problem ……….

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

can you finish the problem……..

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