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March 23, 2020

Area of pinwheel | AMC 8, 2007 | Problem 23

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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