Try this beautiful problem from Geometry based on area of pinwheel.
What is the area of the shaded pinwheel shown in the \(5 \times 5\) grid?
Geometry
Triangle
Square
Answer:$6$
AMC-8 (2007) Problem 23
Pre College Mathematics
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
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