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AMC-8 Geometry Math Olympiad USA Math Olympiad

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?

Area of pinwheel
  • $8$
  • $6$
  • $9$

Key Concepts


Geometry

Triangle

Square

Check the Answer


Answer:$6$

AMC-8 (2007) Problem 23

Pre College Mathematics

Try with Hints


Find the area of white space

Area of pinwheel- solution

Can you now finish the problem ……….

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

can you finish the problem……..

Area of pinwheel- solution

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

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