Blue + Green = Turquoise

Geometry Level 1

ABCD is a unit square, with E the midpoint of AB and F the midpoint of CD. Draw the isosceles triangles ABF and DEC, which intersect at points G and H. What is the area of the diamond-shaped quadrilateral EGFH?

1 5 \frac{1}{5} 1 3 \frac{1}{3} 2 5 \frac{2}{5} 1 4 \frac{1}{4}

Chung Kevin by Chung Kevin , 45, Australia

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2 solutions

The diamond shape is composed of two non-overlapping triangles each with base length 1 2 \dfrac{1}{2} and height 1 2 . \dfrac{1}{2}. Thus their combined area is 2 ∗ ( 1 2 ) 3 = 1 4 . 2*(\dfrac{1}{2})^{3} = \boxed{\dfrac{1}{4}}.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Md Hasib
Apr 1, 2015

There are 8 triangles . This is the information you need to know to do this one.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Though we still need to show that the 8 triangles have the same area.

Chung Kevin - 6 years, 2 months ago

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That's given by the fact that E and F are midpoints.

Karen Black - 6 years, 2 months ago

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