Pink Area.

Geometry Level 2

Each of the four pink triangles has one of their vertices at a corner of the blue square.

What percentage of the square is pink?

15 25 30 35 40

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Ram Mohith
Sep 6, 2018

Let's assume that each tile is a unit square. There 25 such tiles in the blue square. So, area of blue square is 25 \boxed{\color{#3D99F6}25} . Area of all four triangles :

( 1 2 × 2 × 3 ) A + ( 1 2 × 2 × 1 ) B + ( 1 2 × 2 × 2 ) C + ( 1 2 × 3 × 1 ) D \left(\dfrac12 \times 2 \times 3 \right)_A + \left(\dfrac12 \times 2 \times 1 \right)_B + \left(\dfrac12 \times 2 \times 2 \right)_C + \left(\dfrac12 \times 3 \times 1 \right)_D

⟹ A r e a = 3 + 1 + 2 + 1.5 = 7.5 \implies Area = 3 + 1 + 2 + 1.5 = \boxed{\color{#E81990}7.5}

Percentage pink = 7.5 25 × 100 = 30 % \dfrac{\color{#E81990}7.5}{\color{#3D99F6}25} \times 100 = \boxed{\color{#20A900}30 \text{\%}}

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Thank you, nice solution.

Hana Wehbi - 2 years, 9 months ago

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This is a beautiful question but I am feeling sad that this question is not featured in the problems of the week still now.

Ram Mohith - 2 years, 8 months ago

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Thank you, no worries. I also like the ones that are featured every week, they are really good.

Hana Wehbi - 2 years, 8 months ago

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