Medium Portion

Geometry Level 1

Lines A D , B E , AD, BE, and C F CF are medians of triangle A B C ABC , and the yellow area is 47 47 , how much is the blue area?


The answer is 94.

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3 solutions

The three medians divide the triangle into six smaller triangles of equal area. Since the yellow area has 2 2 triangles, the area of one triangle is 47 2 = 23.5 \dfrac{47}{2}=23.5 . The blue area has 4 4 triangles, so the area of the blue area is 4 ( 23.5 ) = 4(23.5)= 94 \boxed{94}

Paola Ramírez
Jul 3, 2017

Medians divide the triangle in six triangles of the same area. The yellow area covers two of the six triangles of the same area \therefore the blue area is twice than yellow area \Rightarrow the blue area is 47 × 2 = 94 47\times 2=94

Marta Reece
Jun 15, 2017

A O B \triangle AOB and A C B \triangle ACB have the same base, A B AB , and their heights are in proportion 3 : 1 3:1 since C F = 3 × O F CF=3\times OF .

Area [ A B C ] = 3 × [ A O B ] [ABC]=3\times\color{#CEBB00}[AOB]

[ b l u e ] \color{#3D99F6}[blue] = [ A B C ] [ A O B ] =[ABC]-\color{#CEBB00}[AOB] = 2 × [ A O B ] =2\times\color{#CEBB00}[AOB] = 2 × 47 = 94 =2\times47=\boxed{94}

Actually medians divide A B C \triangle ABC into six triangles of equal area, in this case four of them are blue and two yellow.

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