trapezoid and circle

**Dragon** · December 15th 2006, 07:34 PM

An isosceles trapezoid is inscribed in a semi circle as shown below such that the nonshaded regions are congruent the radius of the semi circle is one meter. How many square meters are in the area of the trapezoid?

**earboth** · December 15th 2006, 09:39 PM

Originally Posted by Dragon

An isosceles trapezoid is inscribed in a semi circle as shown below such that the nonshaded regions are congruent the radius of the semi circle is one meter. How many square meters are in the area of the trapezoid?

Hello,

the shaded area is the half of a regular(?) hexagon.

The area of this hexagon consists of 6 triangles:

$A_{6-gon}=6 \cdot \frac{1}{2} \cdot a \cdot \underbrace{\frac{1}{2} \cdot a \sqrt{3}}_{\text{height of triangle}}=\frac{3}{2} \cdot a^2 \cdot \sqrt{3}$

The sides of your trapezoid are 1 m, the base has the length 2 m.

The area is the half of the hexagon's area.

$A_{trapezoid}=\frac{3}{4} \cdot 1^2 \cdot \sqrt{3}=\frac{3}{4} \sqrt{3} \approx 1.299 m^2$

EB

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