What fraction of the Rectangle is shaded?

Geometry Level 2

The top of the arrow is at the midpoint A A of the rectangle's edge. What fraction of the rectangle is the blue area which is the area of the arrow?

1 6 \frac{1}{6} 1 10 \frac{1}{10} 1 2 \frac{1}{2} 1 5 \frac{1}{5} 1 4 \frac{1}{4}

Hana Wehbi by Hana Wehbi , 51, USA

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2 solutions

David Vreken
Feb 24, 2018

The shaded area can be cut (along the large rectangle's congruent quadrants) and then rearranged by the following steps:

The shaded area is therefore 1 4 \boxed{\frac{1}{4}} of the area of the large rectangle.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice solution. Thank you.

Hana Wehbi - 3 years, 3 months ago

Let's call the sides of the rectangle x and y. To find the blue area use the blue and white inner triangle to find the blue area: 1/2 xy - 1/4 xy = 1/4 xy. So the blue area is 1/4 of the area of the rectangle

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you.

Hana Wehbi - 3 years, 3 months ago

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