# trapezoid and circle

• Dec 15th 2006, 08:34 PM
Dragon
trapezoid and circle
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?
• Dec 15th 2006, 10:39 PM
earboth
Quote:

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